{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Copy of Template_for CIS521_midterm_2_notes.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "brNDGX-kvzds"
      },
      "source": [
        "# Template for Notes for CIS 521 Midterm 2\n",
        "\n",
        "The midterm exam for CIS 521 will be **open notes**. No other matierals are allowed for the exam - you may not use the textbook, the internet, a Python envionement, or communicate with anyone during the exam. \n",
        "\n",
        "This python notebook is where you should save all of your notes.  It provides a structured template that allows you to add summaries for each of the textbook sections that are part of the required reading, plus room for lecture notes and definitions.\n",
        "\n",
        "Your summaries must be written in your own words.  Do not copy and paste from the textbook.  Do not share your notes with classmates, or copy any of your classmates' notes.  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aPtM8g7R0Pds"
      },
      "source": [
        "# Instructions\n",
        "\n",
        "1. Make a copy of this Google Colab file. From the colab menu, pick **File > Save a copy in Drive**.  That will save a copy of this notebook in your Google drive.\n",
        "2. Go through each section of the notebook, and fill in all the summaries for each chapter and its corresponding sections.  Be sure to save your work frequently!\n",
        "3. Read the notes below about how you can format your summaries.\n",
        "4. In addition to these notes, you are allowed 1 page (both sides) for figures or handwritten notes.\n",
        "5. Submit your version of this notebook to Gradescope before you start the exam.\n",
        "6. If you are taking the exam in person, then you must print a copy of your notes for yourself.   Here's how to print: \n",
        "* Run the last cell of this notebook\n",
        "* Click the \"Mirror cell in tab\" button (this is located in the upper right corner of the cell, immediately to the right of the trash can).  This will open the cell.  \n",
        "* In Chrome, you can then print your notes using the **File > Print** option from the browser's menu.  \n",
        "* In the print options, change the layout from Landscape to Portrait. \n",
        "* Clicking the Save, will save a PDF that you can then print.\n",
        "\n",
        "## Formatting Notes\n",
        "\n",
        "1. The max length for each section's summary is 500 words / 3000 characters.\n",
        "2. You can also write a 2000 word summary of the lectures for each module.\n",
        "3. You may also write definitions of concepts for each module.  The definitions should be written in your own words (not copy and pasted), and they should be no more than 20 words long for each concept. \n",
        "2. You can use Markdown formatting for your summaries. \n",
        "3. You can use Latex formatting for equations. Put two dollar signs before and after your equation like this: \n",
        "$$ \\epsilon = \\frac{1}{mc^2} $$\n",
        "4. When you write python code or psuedocode algorithms, you should surround it with triple backticks like this:\n",
        "```\n",
        "def function():\n",
        "      print('hello world')\n",
        "```\n",
        "5. Write \\ whenever you want to keep writing on the next line without a newline being inserted."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cw5IpDLCZa4W"
      },
      "source": [
        "## Example summary\n",
        "\n",
        "This is a sample summary of [Section 2.1.1](https://web.stanford.edu/~jurafsky/slp3/2.pdf ) of Jurfasky and Martin's Speech and Language Processing's book\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lzaavW96tcxM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6945e100-1167-4d0b-f01e-6e9210a13053"
      },
      "source": [
        "chapter_2_1_example = \"\"\"\n",
        "Regular expressions are an algebraic notation for characterizing \\\n",
        "a set of strings that are useful for searching for a pattern or through a corpus.\\\n",
        "Only the first matching result will be shown. The search string is case sensitive, \\\n",
        "but it can consist of a single character or a sequence of characters. \\\n",
        "While square braces specify a disjunction of characters, the dash can more easily look \\\n",
        "for characters over a range. The caret specifies the non-existence of a character. \\\n",
        "Additionally, the (?) is used to for flexibility on a single character, meaning \\\n",
        "\"the preceding character or nothing\". More importantly, the Kleene star means zero or \\\n",
        "more occurrences of the immediately previous character or regular expression in square braces.\\\n",
        "...\n",
        "\"\"\"\n",
        "\n",
        "length = len(chapter_2_1_example.split(\" \"))\n",
        "print(\"The example summary is {len} words long, so you could write an additional \\\n",
        "{remaining} words.\".format(len=length, remaining=(500-length)))"
      ],
      "execution_count": 113,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The example summary is 116 words long, so you could write an additional 384 words.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s3Uk9gQTevcj"
      },
      "source": [
        "## Example summary length\n",
        "\n",
        "The maximum summary length for each section is 500 words / 3000 characters.  Hopefully you'll find that to be quite generous. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8DvZ57A-djo1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "a5bf8e42-eabe-4256-ade3-1a5e117202b5"
      },
      "source": [
        "# This is an example of a 500 word placeholder\n",
        "placeholder = \"\"\"ultrices vitae auctor eu augue ut lectus arcu bibendum at varius \\\n",
        " vel pharetra vel turpis nunc eget lorem dolor sed viverra ipsum nunc aliquet \\\n",
        " bibendum enim facilisis gravida neque convallis a cras semper auctor neque vitae \\\n",
        " tempus quam pellentesque nec nam aliquam sem et tortor consequat id porta nibh \\\n",
        " venenatis cras sed felis eget velit aliquet sagittis id consectetur purus ut \\\n",
        " faucibus pulvinar elementum integer enim neque volutpat ac tincidunt vitae semper \\ \n",
        " quis lectus nulla at volutpat diam ut venenatis tellus in metus vulputate eu \\\n",
        " scelerisque felis imperdiet proin fermentum leo vel orci porta non pulvinar neque \\ \n",
        " laoreet suspendisse interdum consectetur libero id faucibus nisl tincidunt eget \\\n",
        " nullam non nisi est sit amet facilisis magna etiam tempor orci eu lobortis \\\n",
        " elementum nibh tellus molestie nunc non blandit massa enim nec dui nunc mattis \\\n",
        " enim ut tellus elementum sagittis vitae et leo duis ut diam quam nulla porttitor \\\n",
        " massa id neque aliquam vestibulum morbi blandit cursus risus at ultrices mi tempus \\\n",
        " imperdiet nulla malesuada pellentesque elit eget gravida cum sociis natoque \\\n",
        " penatibus et magnis dis parturient montes nascetur ridiculus mus mauris vitae \\\n",
        " ultricies leo integer malesuada nunc vel risus commodo viverra maecenas accumsan \\\n",
        " lacus vel facilisis volutpat est velit egestas dui id ornare arcu odio ut sem nulla \\\n",
        " pharetra diam sit amet nisl suscipit adipiscing bibendum est ultricies integer \\\n",
        " quis auctor elit sed vulputate mi sit amet mauris commodo quis imperdiet massa \\\n",
        " tincidunt nunc pulvinar sapien et ligula ullamcorper malesuada proin libero nunc \\\n",
        " consequat interdum varius sit amet mattis vulputate enim nulla aliquet porttitor \\\n",
        " lacus luctus accumsan tortor posuere ac ut consequat semper viverra nam libero \\\n",
        " justo laoreet sit amet cursus sit amet dictum sit amet justo donec enim diam \\\n",
        " vulputate ut pharetra sit amet aliquam id diam maecenas ultricies mi eget mauris \\\n",
        " pharetra et ultrices neque ornare aenean euismod elementum nisi quis eleifend quam \\\n",
        " adipiscing vitae proin sagittis nisl rhoncus mattis rhoncus urna neque viverra justo \\\n",
        " nec ultrices dui sapien eget mi proin sed libero enim sed faucibus turpis in \\\n",
        " eu mi bibendum neque egestas congue quisque egestas diam in arcu cursus euismod \\\n",
        " quis viverra nibh cras pulvinar mattis nunc sed blandit libero volutpat sed cras \\\n",
        " ornare arcu dui vivamus arcu felis bibendum ut tristique et egestas quis ipsum \\\n",
        " suspendisse ultrices gravida dictum fusce ut placerat orci nulla pellentesque \\\n",
        " dignissim enim sit amet venenatis urna cursus eget nunc scelerisque viverra mauris \\\n",
        " in aliquam sem fringilla ut morbi tincidunt augue interdum velit euismod in \\\n",
        " pellentesque massa placerat duis ultricies lacus sed turpis tincidunt id aliquet \\\n",
        " risus feugiat in ante metus dictum at tempor commodo ullamcorper a lacus vestibulum \\\n",
        " sed arcu non odio euismod lacinia at quis risus sed vulputate odio ut enim blandit \\\n",
        " volutpat maecenas volutpat blandit aliquam etiam erat velit scelerisque in \\\n",
        " dictum non consectetur a erat nam at lectus urna\"\"\"\n",
        "\n",
        "print(\"The length in words is\", len(placeholder.split(' ')))\n",
        "print(\"The length in characters is\", len(placeholder))"
      ],
      "execution_count": 114,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The length in words is 500\n",
            "The length in characters is 3030\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5yG3-YncJfTB"
      },
      "source": [
        "# Permissions to use your summaries\n",
        "\n",
        "We'd like to use your summaries to help develop better educational resources like [remember.school](https://remember.school) or a question-answering system about the textbook.  \n",
        "\n",
        "1. Please enter your name.  \n",
        "\n",
        "2. If you grant permission for us to use your summaries under a [Creative Commons License](https://creativecommons.org/licenses/by/4.0/), please set ```permission = True```.  If you do not grant permission, please set it to false. Your answer won't affect your grade.\n",
        "\n",
        "3. If you grant us permission, and you'd like to remain anonymous, set ```anonymous = True```.  We'll remove your name before sharing your summaries with anyone. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2RECnJArJew4"
      },
      "source": [
        "name = \"\"\n",
        "permission = True\n",
        "anonymous = False"
      ],
      "execution_count": 115,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GZZXyrV-xuAp"
      },
      "source": [
        "# Module 8 - Markov Decision Process"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y2NfE1CKxzS-"
      },
      "source": [
        "# Russell and Norvig, AIMA Chapter 16, “Making Simple Decisions” (16.1-16.3)\n",
        "\n",
        "sample_equation = r\"\"\" $P(\\textnormal{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$ \"\"\"\n",
        "\n",
        "chapter16_1 = \"\"\" Chapter 16.1 summary. \"\"\"  + sample_equation\n",
        "chapter16_2 =  \"\"\" Your summary here \"\"\"\n",
        "chapter16_3 =  \"\"\" Your summary here \"\"\"\n",
        "\n",
        "\n",
        "# Russell and Norvig, AIMA Chapter 17, “Making Complex Decision” (17.1-17.2)\n",
        "chapter17_1 = \"\"\" Your summary here \"\"\"\n",
        "chapter17_2 =  \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Lecture notes \n",
        "module8_lecture_notes = \"\"\"\n",
        "- MDP is sequential decision problem, fully observable, stochastic, additive rewards\\n\n",
        "- What is needed\\n\n",
        "   - Set of states\n",
        "   - Set of actions\n",
        "   - Stochastic transition model\n",
        "   - Reward function\n",
        "   - Initial state\n",
        "   - Optional: terminal states\n",
        "- Performance of MDP is sum of the rewards for the transitons it takes\n",
        "- Discounting utilities: $\\Sigma_{t=0}^{inf}\\gamma^tr_t \\leq R_{max}/(1-\\gamma)$\n",
        "- $V^*(s)$ = expected utility starting in s and acting optimally\n",
        "- $Q^*(s,a)$ = expected utility starting out having raken action a from state s and then acting optimally\n",
        "- $\\pi^*(s)$ = optimal action from state s\n",
        "\n",
        "- Value iteration:\n",
        "- Start w/ V_0(s)=0 and then apply Bellman update until convergence\n",
        "- Each iteration is O(S^2A)\n",
        "- Will always converge\n",
        "- Larger discount value $\\gamma$ means it takes longer to converge\n",
        "-\n",
        "- Policy evaluation:\n",
        "- $V^{\\pi}(s)=$ expected total disconted rewards starting in s and following $\\pi$\n",
        "- Start at V_0^pi(s) = 0 and then apply Bellman update\n",
        "- Idea 1: Turn recursive Bellman equations into updates\n",
        "- Idea 2: Bellman euations are a linear system\n",
        "- O(S^2) per iteration\n",
        "\n",
        "- Policy extraction: Take argmax\n",
        "\n",
        "- Policy iteration:\n",
        "1. Policy evaluation: calculate utilities for some fixed policy until convergence\n",
        "2. Policy improvement: update policy using one-step look-ahead w/ resulting converged utilities as future values\n",
        "3. Repeat until policy converges\n",
        "\n",
        "- Utility\n",
        "- Axioms of Rationality\n",
        "1. Orderability: (A > B) V (B > A) V (A ~ B)\n",
        "2. Transitivity: (A > B) V (B > C) => (A > C)\n",
        "3. Continuity: A > B > C => there exists a p st [p,A; 1-p,C] ~ B\n",
        "4. Substitutability: A ~ B => [p,A; 1-p,C] ~ [p,B; 1-p,C]\n",
        "5. Monotonicity: A > B => (p >= q <=> [p,A; 1-p,B] >= [q,A; 1-q, B])\n",
        "- Theorem: Rational preferences imply behavior describable as maximization of expected utility\n",
        "- MEU Principle: Choose action that maximizes expected utility\n",
        "   \"\"\"\n",
        "\n",
        "\n",
        "# Definitions of concepts from Module 8.\n",
        "# You can define any term in the textbook or lecture, \n",
        "# but you most use your own words for the definitions.\n",
        "# Each definition should be at most 25 words long.\n",
        "\n",
        "module8_definitions = {\n",
        "\"utility function\" : \"Your definition here\",\n",
        "\"expected utility\" : \"your definition here\",\n",
        "\"etc.\": \"your definition here\",\n",
        "}\n",
        "\n"
      ],
      "execution_count": 116,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "elCCgY64spuq"
      },
      "source": [
        "## Preview of your notes for Module 8\n",
        "\n",
        "Here's a preview of your how your notes will be displayed.  At the end of this Python notebook, we'll aggregate your notes for all modules together into a single display.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gYYeNcdM_maE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1454
        },
        "outputId": "47aef70b-86e0-404c-ff99-f80e9070a399"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "from IPython.display import display, Markdown, Latex\n",
        "\n",
        "module8_sections = [\n",
        "  (\"AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\", chapter16_1),\n",
        "  (\"AIMA Chapter 16.2 The Basis of Utility Theory\", chapter16_2),\n",
        "  (\"AIMA Chapter 16.3 Utility Functions\", chapter16_3),\n",
        "  (\"AIMA Chapter 17.1 Sequential Decision Problems\", chapter17_1),\n",
        "  (\"AIMA Chapter 17.2 Algorithms for MDPs\", chapter17_2),\n",
        "  (\"Module 8 Lecture Notes\", module8_lecture_notes),\n",
        "]\n",
        "\n",
        "\n",
        "def length_check(sections):\n",
        "  warnings = \"\"\n",
        "  for section, summary in sections:\n",
        "    max_word_length = 500\n",
        "    max_character_length = 3000\n",
        "    if \"lecture\" in section.lower():\n",
        "      # It's OK to do longer summaries of the lectures\n",
        "      max_word_length = 2000\n",
        "      max_character_length = 12000  \n",
        "    if (len(summary) > max_character_length or len(summary.split(' ')) > max_word_length):\n",
        "      warnings += \"WARNING: Your summary of '{section}' is too long!\\n\".format(section=section)\n",
        "  return warnings\n",
        "\n",
        "def length_check_definitions(definitions):\n",
        "  warnings = \"\"\n",
        "  for concept, definition in definitions.items():\n",
        "    if(len(definition.split(' ')) > 25):\n",
        "      warnings += \"WARNING: Your definition of '{concept}' is too long!\\n\".format(concept=concept)\n",
        "  return warnings\n",
        "\n",
        "\n",
        "def format_module(module_num, title, sections, definitions, show_placeholder=False):\n",
        "  markdown = \"\"\n",
        "\n",
        "  # Check summary lengths\n",
        "  warnings = length_check(sections)\n",
        "  if warnings != \"\":\n",
        "    markdown += \"## \" + warnings\n",
        "\n",
        "  # Check definition lengths\n",
        "  warnings = length_check_definitions(definitions)\n",
        "  if warnings != \"\":\n",
        "    markdown += \"## \" + warnings\n",
        "\n",
        "  markdown += \"# Module {num}: {title}\\n\".format(num=module_num, title=title)\n",
        "\n",
        "\n",
        "  for section, summary in sections:\n",
        "    if show_placeholder and summary == \" Your summary here \":\n",
        "      summary = placeholder\n",
        "    markdown += \"## {section}\\n{summary}\\n\\n\".format(section=section, summary=summary)\n",
        "  \n",
        "  markdown += \"## Module {num} Definitions\\n\".format(num=module_num)\n",
        "  for concept, definition in definitions.items():\n",
        "    markdown += \"* **{concept}** - {definition}\\n\".format(concept=concept.capitalize(), definition=definition)\n",
        "  return markdown\n",
        "\n",
        "\n",
        "module8_markdown = format_module(8, \"Markov Decision Processes\", module8_sections, module8_definitions)\n",
        "display(Markdown(module8_markdown))"
      ],
      "execution_count": 117,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 8: Markov Decision Processes\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n Chapter 16.1 summary.  $P(\\textnormal{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$ \n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n Your summary here \n\n## AIMA Chapter 16.3 Utility Functions\n Your summary here \n\n## AIMA Chapter 17.1 Sequential Decision Problems\n Your summary here \n\n## AIMA Chapter 17.2 Algorithms for MDPs\n Your summary here \n\n## Module 8 Lecture Notes\n\n- MDP is sequential decision problem, fully observable, stochastic, additive rewards\n\n- What is needed\n\n   - Set of states\n   - Set of actions\n   - Stochastic transition model\n   - Reward function\n   - Initial state\n   - Optional: terminal states\n- Performance of MDP is sum of the rewards for the transitons it takes\n- Discounting utilities: $\\Sigma_{t=0}^{inf}\\gamma^tr_t \\leq R_{max}/(1-\\gamma)$\n- $V^*(s)$ = expected utility starting in s and acting optimally\n- $Q^*(s,a)$ = expected utility starting out having raken action a from state s and then acting optimally\n- $\\pi^*(s)$ = optimal action from state s\n\n- Value iteration:\n- Start w/ V_0(s)=0 and then apply Bellman update until convergence\n- Each iteration is O(S^2A)\n- Will always converge\n- Larger discount value $\\gamma$ means it takes longer to converge\n-\n- Policy evaluation:\n- $V^{\\pi}(s)=$ expected total disconted rewards starting in s and following $\\pi$\n- Start at V_0^pi(s) = 0 and then apply Bellman update\n- Idea 1: Turn recursive Bellman equations into updates\n- Idea 2: Bellman euations are a linear system\n- O(S^2) per iteration\n\n- Policy extraction: Take argmax\n\n- Policy iteration:\n1. Policy evaluation: calculate utilities for some fixed policy until convergence\n2. Policy improvement: update policy using one-step look-ahead w/ resulting converged utilities as future values\n3. Repeat until policy converges\n\n- Utility\n- Axioms of Rationality\n1. Orderability: (A > B) V (B > A) V (A ~ B)\n2. Transitivity: (A > B) V (B > C) => (A > C)\n3. Continuity: A > B > C => there exists a p st [p,A; 1-p,C] ~ B\n4. Substitutability: A ~ B => [p,A; 1-p,C] ~ [p,B; 1-p,C]\n5. Monotonicity: A > B => (p >= q <=> [p,A; 1-p,B] >= [q,A; 1-q, B])\n- Theorem: Rational preferences imply behavior describable as maximization of expected utility\n- MEU Principle: Choose action that maximizes expected utility\n   \n\n## Module 8 Definitions\n* **Utility function** - Your definition here\n* **Expected utility** - your definition here\n* **Etc.** - your definition here\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9xRbdqDox2zD"
      },
      "source": [
        "#Module 9 - Reinforcement Learning"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DpBvu7EMx7sy"
      },
      "source": [
        "# Russell and Norvig, AIMA Section 17.3 “Bandit Problems”\n",
        "chapter17_3 =  \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Russell and Norvig, AIMA Chapter 22 “Reinforcement Learning” (Sections 22.1-22.5)\n",
        "chapter22_1 =  \"\"\" Your summary here \"\"\"\n",
        "chapter22_2 =  \"\"\" Your summary here \"\"\"\n",
        "chapter22_3 =  \"\"\" Your summary here \"\"\"\n",
        "chapter22_4 =  \"\"\" Your summary here \"\"\"\n",
        "chapter22_5 =  \"\"\" Your summary here \"\"\"\n",
        "\n",
        "\n",
        "# Lecture notes \n",
        "module9_lecture_notes = \"\"\"\n",
        "- Solving MDPs is offline planning\n",
        "- Online planning is solving as you go (learning)\n",
        "  - Exploration\n",
        "  - Exploitation\n",
        "  - Regret\n",
        "  - Sampling\n",
        "  - Difficulty\n",
        "- Reinforcement is solving an MDO when you don't know transition model T or reward function R\n",
        "\n",
        "Model-based learning:\n",
        "- Learn empirical MDP model by trying stuff out and counting outcomes s' for each s,a\n",
        "- Normalize the resulting transaction and reward for each s,a\n",
        "- Solve this MDP \n",
        "\n",
        "Passive reinforcement learning:\n",
        "- Fixed policy pi(s) and learn the state values from experience\n",
        "- Direct evaluation: Average those samples\n",
        "- Pros: easy to understand, model free, eventually computes correct avg values\n",
        "- Cons: wastes info about state connections, each state must be learned separately, long time\n",
        "- Instead, temporal difference learning: learn form every experience\n",
        "\n",
        "Temporal difference learning\n",
        "- Update V(s) for each transition we experience (s, a, s', r)\n",
        "- Move values toward value of whatever successor occurs: running avg\n",
        "  - Sample of V(s): sample = R(s,pi(s),s') + gammeV^pi(s')\n",
        "  - Update to V(s): V^pi(s) <- (1-a)V^pi(s) + alpha*sample\n",
        "  - Same update: V^pi(s) <- V^pi(s) + alpha*(sample - V^pi(s))\n",
        "- Exponential moving avg: $\\bar{x}_n = (1-\\alpha)\\bar{x}_{n-1} + \\alpha x_n$\n",
        "- $alpha$ is learning rate: how much you trust new observations\n",
        "- Problem: can't learn policy moves\n",
        "\n",
        "Q-Learning\n",
        "- Sample-based Q-value iteration\n",
        "  - Receive a sample (s,a,s',r)\n",
        "  - Consider your old estimate Q(s,a)\n",
        "  - Consider your new sample estimate $sample = R(s,a,s') + \\gamma max_{a'}Q(s',a')$\n",
        "  - Incorporate the new estimate into a running avg $Q(s,a) \\leftarrow (1-\\alpha)Q(s,a) + \\alpha sample$\n",
        "- Converges to optimal policy even if acting suboptimally, but\n",
        "  - Need to explore enough and make learning rate small enough (but don't decrease too quickly)\n",
        "\n",
        "Exploration vs Exploitation\n",
        "- Exploration function: Takes a value estimate u and a visit count n and returns an optimistic utility\n",
        "   - Ex. f(u,n) = u + k/n\n",
        "- Modified Q-update: $Q(s,a) <-_{\\alpha} R(s,a,s') + \\gamma max_{a'}f(Q(s',a'), N(s',a'))$\n",
        "- Regret: Measure of total mistakes (difference between expected rewards and optimal expected rewards)\n",
        "- Minimizing regret requires optimally learning to be optimal\n",
        "- Random exploration has more regret over exploration functions\n",
        "\n",
        "Approximate Q-Learning\n",
        "- Evaluation function: ideally returns actual minimax value of the position\n",
        "- In practice: typically a weighted linear sum of features\n",
        "  - Eval(s) = w1*f1(s) + q2*f2(s) + ...wn*fn(s)\n",
        "- Use this to write a Q-function (or value function) for any state using a few weights\n",
        "  - Only an approximation\n",
        "  - Learning alg exstimates weights\n",
        "- $Q(s,a) = w_1f_1(s,a) + ... +w_nf_n(s,a)$\n",
        "- Q-learning with linear functions:\n",
        "  - transition = (s,a,r,s')\n",
        "  - difference = [r + $\\gamma max_a$ Q(s',a')] - Q(s,a) = (reward + estimate of future reward) - previous estimate of how valuable this state is\n",
        "  - $w_i = w_i + \\alpha (difference)f_i(s,a)\n",
        "- Essentially online OLS\n",
        "\"\"\"\n",
        "\n",
        "# Each definition should be at most 25 words long.\n",
        "module9_definitions = {\n",
        "\"term\" : \"your definition here\",\n",
        "}"
      ],
      "execution_count": 118,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ydOK__lwWgdp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1662
        },
        "cellView": "form",
        "outputId": "97d9f596-a6f2-457a-a1e2-4a3b05555e6a"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "\n",
        "module9_sections = [\n",
        "  (\"AIMA Chapter 17.3 Bandit Problems\", chapter17_3),\n",
        "  (\"AIMA Chapter 22.1 Learning from Rewards\", chapter22_1),\n",
        "  (\"AIMA Chapter 22.2 Passive Reinforcement Learning\", chapter22_2),\n",
        "  (\"AIMA Chapter 22.3 Active Reinforcement Learning\", chapter22_3),\n",
        "  (\"AIMA Chapter 22.4 Generalization in Reinforcement Learning\", chapter22_4),\n",
        "  (\"Module 9 Lecture Notes\", module9_lecture_notes),\n",
        "]\n",
        "\n",
        "module9_markdown = format_module(9, \"Reinforcement Learning\", module9_sections, module9_definitions)\n",
        "display(Markdown(module9_markdown))"
      ],
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 9: Reinforcement Learning\n## AIMA Chapter 17.3 Bandit Problems\n Your summary here \n\n## AIMA Chapter 22.1 Learning from Rewards\n Your summary here \n\n## AIMA Chapter 22.2 Passive Reinforcement Learning\n Your summary here \n\n## AIMA Chapter 22.3 Active Reinforcement Learning\n Your summary here \n\n## AIMA Chapter 22.4 Generalization in Reinforcement Learning\n Your summary here \n\n## Module 9 Lecture Notes\n\n- Solving MDPs is offline planning\n- Online planning is solving as you go (learning)\n  - Exploration\n  - Exploitation\n  - Regret\n  - Sampling\n  - Difficulty\n- Reinforcement is solving an MDO when you don't know transition model T or reward function R\n\nModel-based learning:\n- Learn empirical MDP model by trying stuff out and counting outcomes s' for each s,a\n- Normalize the resulting transaction and reward for each s,a\n- Solve this MDP \n\nPassive reinforcement learning:\n- Fixed policy pi(s) and learn the state values from experience\n- Direct evaluation: Average those samples\n- Pros: easy to understand, model free, eventually computes correct avg values\n- Cons: wastes info about state connections, each state must be learned separately, long time\n- Instead, temporal difference learning: learn form every experience\n\nTemporal difference learning\n- Update V(s) for each transition we experience (s, a, s', r)\n- Move values toward value of whatever successor occurs: running avg\n  - Sample of V(s): sample = R(s,pi(s),s') + gammeV^pi(s')\n  - Update to V(s): V^pi(s) <- (1-a)V^pi(s) + alpha*sample\n  - Same update: V^pi(s) <- V^pi(s) + alpha*(sample - V^pi(s))\n- Exponential moving avg: $\bar{x}_n = (1-\u0007lpha)\bar{x}_{n-1} + \u0007lpha x_n$\n- $alpha$ is learning rate: how much you trust new observations\n- Problem: can't learn policy moves\n\nQ-Learning\n- Sample-based Q-value iteration\n  - Receive a sample (s,a,s',r)\n  - Consider your old estimate Q(s,a)\n  - Consider your new sample estimate $sample = R(s,a,s') + \\gamma max_{a'}Q(s',a')$\n  - Incorporate the new estimate into a running avg $Q(s,a) \\leftarrow (1-\u0007lpha)Q(s,a) + \u0007lpha sample$\n- Converges to optimal policy even if acting suboptimally, but\n  - Need to explore enough and make learning rate small enough (but don't decrease too quickly)\n\nExploration vs Exploitation\n- Exploration function: Takes a value estimate u and a visit count n and returns an optimistic utility\n   - Ex. f(u,n) = u + k/n\n- Modified Q-update: $Q(s,a) <-_{\u0007lpha} R(s,a,s') + \\gamma max_{a'}f(Q(s',a'), N(s',a'))$\n- Regret: Measure of total mistakes (difference between expected rewards and optimal expected rewards)\n- Minimizing regret requires optimally learning to be optimal\n- Random exploration has more regret over exploration functions\n\nApproximate Q-Learning\n- Evaluation function: ideally returns actual minimax value of the position\n- In practice: typically a weighted linear sum of features\n  - Eval(s) = w1*f1(s) + q2*f2(s) + ...wn*fn(s)\n- Use this to write a Q-function (or value function) for any state using a few weights\n  - Only an approximation\n  - Learning alg exstimates weights\n- $Q(s,a) = w_1f_1(s,a) + ... +w_nf_n(s,a)$\n- Q-learning with linear functions:\n  - transition = (s,a,r,s')\n  - difference = [r + $\\gamma max_a$ Q(s',a')] - Q(s,a) = (reward + estimate of future reward) - previous estimate of how valuable this state is\n  - $w_i = w_i + \u0007lpha (difference)f_i(s,a)\n- Essentially online OLS\n\n\n## Module 9 Definitions\n* **Term** - your definition here\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "46MQLR-Gx8dZ"
      },
      "source": [
        "#Module 10 - Probabilities and Language Models"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BN0b1eVYx-nd"
      },
      "source": [
        "# Russell and Norvig, AIMA 4th Edition, AIMA Chapter 12 “Quantifying Uncertainty” (Sections 12.1-12.7)\n",
        "chapter12_1 = \"\"\" Your summary here \"\"\"\n",
        "chapter12_2 = \"\"\" Your summary here \"\"\"\n",
        "chapter12_3 = \"\"\" Your summary here \"\"\"\n",
        "chapter12_4 = \"\"\" Your summary here \"\"\"\n",
        "chapter12_5 = \"\"\" Your summary here \"\"\"\n",
        "chapter12_6 = \"\"\" Your summary here \"\"\"\n",
        "chapter12_7 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "\n",
        "# Jurafsky and Martin, Speech and Language Processing Chapter 3 “N-Gram Language Models”  (Sections 3.1-3.5,3.7)\n",
        "SLP_chapter3_1 = \"\"\" Your summary here \"\"\"\n",
        "SLP_chapter3_2 = \"\"\" Your summary here \"\"\"\n",
        "SLP_chapter3_3 = \"\"\" Your summary here \"\"\"\n",
        "SLP_chapter3_4 = \"\"\" Your summary here \"\"\"\n",
        "SLP_chapter3_5 = \"\"\" Your summary here \"\"\"\n",
        "SLP_chapter3_7 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "\n",
        "# Lecture notes \n",
        "module10_lecture_notes = \"\"\"\n",
        "Probababilitistic Inference and Rules\n",
        "- General case\n",
        "  - Evidence variables: E_1 ... E_k = e_1 ... e_k\n",
        "  - Query variable: Q\n",
        "  - Hidden variables: H_1 ... H_r\n",
        "- Want P(Q|e1...e_k)\n",
        "1. Select the entries consistent with the evidence\n",
        "2. Sum at H to get join of Query and evidene\n",
        "  - P(Q, e1...ek) = $\\Sigma_{h1,...,h_r}$P(Q,h1...hr,e1...ek)\n",
        "3. Normalize: Multiply by 1/z\n",
        "  - P(Q|e1...ek) = 1/z * P(Q, e1...ek)\n",
        "\n",
        "Language Models\n",
        "- Get P(w1,w2,...,wn) P(w_i | w1,...,wi-1) using chain rule\n",
        "- Maximum likelihood estimator: count and divide\n",
        "  - P(w_i | w1,...,wi-1) = count(w1,...,wi)/ count(w1,...,wi-1)\n",
        "- Markov assumption: only previous k words matter\n",
        "- n-grams\n",
        "\"\"\"\n",
        "\n",
        "\n",
        "# Each definition should be at most 25 words long.\n",
        "module10_definitions = {\n",
        "\"term\" : \"your definition here\",\n",
        "}"
      ],
      "execution_count": 120,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lvtN3p7ET3Tx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1442
        },
        "cellView": "form",
        "outputId": "e8a7df0c-459c-4deb-bc7c-6f3708f5dcda"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module10_sections = [\n",
        "  (\"AIMA Chapter 12.1 Acting under Uncertainty\", chapter12_1),\n",
        "  (\"AIMA Chapter 12.2 Basic Probability Notation\", chapter12_2),\n",
        "  (\"AIMA Chapter 12.3 Inference Using Full Joint Distributions\", chapter12_3),\n",
        "  (\"AIMA Chapter 12.4 Independence\", chapter12_4),\n",
        "  (\"AIMA Chapter 12.5 Bayes’ Rule and Its Use\", chapter12_5),\n",
        "  (\"AIMA Chapter 12.6 Naive Bayes Models\", chapter12_6),\n",
        "  (\"AIMA Chapter 12.7 The Wumpus World Revisited\", chapter12_7),\n",
        "  (\"SLP Chapter 3.1 N-Grams\", SLP_chapter3_1),\n",
        "  (\"SLP Chapter 3.2 Evaluating Language Models\", SLP_chapter3_2),\n",
        "  (\"SLP Chapter 3.3 Sampling sentences from a language model\", SLP_chapter3_3),\n",
        "  (\"SLP Chapter 3.4 Generalization and Zeros\", SLP_chapter3_4),\n",
        "  (\"SLP Chapter 3.5 Smoothing\", SLP_chapter3_5),\n",
        "  (\"SLP Chapter 3.7 Huge Language Models and Stupid Backoff\", SLP_chapter3_7),\n",
        "  (\"Module 10 Lecture Notes\", module10_lecture_notes),\n",
        "]\n",
        "\n",
        "module10_markdown = format_module(10, \"Probabilies and Language Models\", module10_sections, module10_definitions)\n",
        "display(Markdown(module10_markdown))"
      ],
      "execution_count": 121,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 10: Probabilies and Language Models\n## AIMA Chapter 12.1 Acting under Uncertainty\n Your summary here \n\n## AIMA Chapter 12.2 Basic Probability Notation\n Your summary here \n\n## AIMA Chapter 12.3 Inference Using Full Joint Distributions\n Your summary here \n\n## AIMA Chapter 12.4 Independence\n Your summary here \n\n## AIMA Chapter 12.5 Bayes’ Rule and Its Use\n Your summary here \n\n## AIMA Chapter 12.6 Naive Bayes Models\n Your summary here \n\n## AIMA Chapter 12.7 The Wumpus World Revisited\n Your summary here \n\n## SLP Chapter 3.1 N-Grams\n Your summary here \n\n## SLP Chapter 3.2 Evaluating Language Models\n Your summary here \n\n## SLP Chapter 3.3 Sampling sentences from a language model\n Your summary here \n\n## SLP Chapter 3.4 Generalization and Zeros\n Your summary here \n\n## SLP Chapter 3.5 Smoothing\n Your summary here \n\n## SLP Chapter 3.7 Huge Language Models and Stupid Backoff\n Your summary here \n\n## Module 10 Lecture Notes\n\nProbababilitistic Inference and Rules\n- General case\n  - Evidence variables: E_1 ... E_k = e_1 ... e_k\n  - Query variable: Q\n  - Hidden variables: H_1 ... H_r\n- Want P(Q|e1...e_k)\n1. Select the entries consistent with the evidence\n2. Sum at H to get join of Query and evidene\n  - P(Q, e1...ek) = $\\Sigma_{h1,...,h_r}$P(Q,h1...hr,e1...ek)\n3. Normalize: Multiply by 1/z\n  - P(Q|e1...ek) = 1/z * P(Q, e1...ek)\n\nLanguage Models\n- Get P(w1,w2,...,wn) P(w_i | w1,...,wi-1) using chain rule\n- Maximum likelihood estimator: count and divide\n  - P(w_i | w1,...,wi-1) = count(w1,...,wi)/ count(w1,...,wi-1)\n- Markov assumption: only previous k words matter\n- n-grams\n\n\n## Module 10 Definitions\n* **Term** - your definition here\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WHREsHSSyA-h"
      },
      "source": [
        "#Module 11 - Probabilistic Reasoning and Bayes’ Nets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tuFC8w7CyCns"
      },
      "source": [
        "# Russell and Norvig, Russell and Norvig, AIMA Chapter 13 “Probabilistic Reasoning” (13.1, 13.2, 13.3)\n",
        "chapter13_1 = \"\"\" Your summary here \"\"\"\n",
        "chapter13_2 = \"\"\" Your summary here \"\"\"\n",
        "chapter13_3 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "\n",
        "# Lecture notes \n",
        "module11_lecture_notes = \"\"\"\n",
        "- Bayes Nets Assumptions: P(x_i | x_1...x_i-1) = P(x_i | parents(x_i))\n",
        "- Bays Newt: technique for describing complex join distributions using simple, local distributions\n",
        "- DAG graph\n",
        "- P(x | parents(x))\n",
        "- Bayes Net = topology + local conditional probabilities\n",
        "- Size of N-node net if nodes have up to k parents = O(N*2^{k+1})\n",
        "   - Would be O(2^n) as regular joint distribution\n",
        "- (Conditional) independence? X (conditionally) independent of Y (given Z)\n",
        "  - Shade in Z (observed)\n",
        "  - Active paths\n",
        "    - Causal chain: A-> B -> C where B is unobserved (either direction)\n",
        "    - Common cause: A <- B -> C where B is unobserved\n",
        "    - Common effect (V-structure): A -> B <- C where B or one of its descendents is observed\n",
        "  - If at least one active path exists, then not independent. Else, independent.\n",
        "    - Active path is where each triple is active. If one triple along the path is inactive, then path is inactive.\n",
        "- Can run a d-separation alg to build a complete list of conidtional independences of the form X_i ind X_j | X_k1,...,X_k2\n",
        "\n",
        "Inference by enumeration\n",
        "- Given evidence variables, query variable, and hidden variables, get P(Q|e1...ek)\n",
        "  1. Select entries consistent with the variables\n",
        "  2. Sum out H to get joint of query and evidence\n",
        "  3. Normalize\n",
        "- Even in Bayes' Net, this is still slow because we are recreating the joint distributions\n",
        "- NP-hard\n",
        "\"\"\"\n",
        "\n",
        "# Definitions\n",
        "module11_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n"
      ],
      "execution_count": 122,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vqtEs0gHs9sO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 846
        },
        "cellView": "form",
        "outputId": "4393f3d2-3df2-474e-ac9d-8224de9bc5c7"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module11_sections = [\n",
        "  (\"AIMA Chapter 13.1 Representing Knowledge in an Uncertain Domain\", chapter13_1),\n",
        "  (\"AIMA Chapter 13.2 The Semantics of Bayesian Networks\", chapter13_2),\n",
        "  (\"AIMA 13.3 Exact Inference in Bayesian Networks\", chapter13_3),\n",
        "  (\"Module 11 Lecture Notes\", module11_lecture_notes),\n",
        "]\n",
        "\n",
        "module11_markdown = format_module(11, \"Probabilistic Reasoning and Bayes’ Nets\", \n",
        "                         module11_sections, \n",
        "                         module11_definitions)\n",
        "display(Markdown(module11_markdown))"
      ],
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 11: Probabilistic Reasoning and Bayes’ Nets\n## AIMA Chapter 13.1 Representing Knowledge in an Uncertain Domain\n Your summary here \n\n## AIMA Chapter 13.2 The Semantics of Bayesian Networks\n Your summary here \n\n## AIMA 13.3 Exact Inference in Bayesian Networks\n Your summary here \n\n## Module 11 Lecture Notes\n\n- Bayes Nets Assumptions: P(x_i | x_1...x_i-1) = P(x_i | parents(x_i))\n- Bays Newt: technique for describing complex join distributions using simple, local distributions\n- DAG graph\n- P(x | parents(x))\n- Bayes Net = topology + local conditional probabilities\n- Size of N-node net if nodes have up to k parents = O(N*2^{k+1})\n   - Would be O(2^n) as regular joint distribution\n- (Conditional) independence? X (conditionally) independent of Y (given Z)\n  - Shade in Z (observed)\n  - Active paths\n    - Causal chain: A-> B -> C where B is unobserved (either direction)\n    - Common cause: A <- B -> C where B is unobserved\n    - Common effect (V-structure): A -> B <- C where B or one of its descendents is observed\n  - If at least one active path exists, then not independent. Else, independent.\n    - Active path is where each triple is active. If one triple along the path is inactive, then path is inactive.\n- Can run a d-separation alg to build a complete list of conidtional independences of the form X_i ind X_j | X_k1,...,X_k2\n\nInference by enumeration\n- Given evidence variables, query variable, and hidden variables, get P(Q|e1...ek)\n  1. Select entries consistent with the variables\n  2. Sum out H to get joint of query and evidence\n  3. Normalize\n- Even in Bayes' Net, this is still slow because we are recreating the joint distributions\n- NP-hard\n\n\n## Module 11 Definitions\n* **Concept** - definition\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F3FPMzG9yUls"
      },
      "source": [
        "#Module 12 - Naive Bayes and Perceptrons"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iEIOpL7vyWcc"
      },
      "source": [
        "# Russell and Norvig, AIMA Chapter 19 “Learning from Examples” (Sections 19.1-19.6)\n",
        "\n",
        "chapter19_1 = \"\"\" Your summary here \"\"\"\n",
        "chapter19_2 = \"\"\" Your summary here \"\"\"\n",
        "chapter19_3 = \"\"\" Your summary here \"\"\"\n",
        "chapter19_4 = \"\"\" Your summary here \"\"\"\n",
        "chapter19_5 = \"\"\" Your summary here \"\"\"\n",
        "chapter19_6 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Speech and Language Processing Chapter 4 “Naive Bayes and Sentiment Classification”\n",
        "slp_chapter4_1 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_2 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_3 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_4 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_5 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_6 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_7 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_8 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_9 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter4_10 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Lecture notes \n",
        "module12_lecture_notes = \"\"\"\n",
        "- Naitve Bayes: All features are independent effects of the label\n",
        "- General Naive Bayes: P(Y, F_1...F_n) = P(Y)$\\Pi_i$P(F_i|Y)\n",
        "- Total number of parameters is linear in nunmber of features\n",
        "- Inference for Naive Bayes\n",
        "  1. Get joint prob of label and evidence for each label - P(Y_k, f_1...f_n)\n",
        "  2. Sum to get prob of evidence - P(y_k)$\\Pi_i$P(f_i|y_k)\n",
        "  3. Normalize by dividing step 1 by step 2 - P(Y | f_1...f_n)\n",
        "- What we need in Naive Bayes\n",
        "  - Inference Method (above)\n",
        "  - Estimates of local conditional probability table $\\theta$\n",
        "    - Come from training data counts\n",
        "- Important concepts\n",
        "  - Data: Training set, held out set, test set\n",
        "  - Features: attribute-value pairs which characterize each x\n",
        "  - Experimentation cycle\n",
        "    - Learn parameters on training set\n",
        "    - Tune hyperparameters on held-out set\n",
        "    - Compute accuracy of test set\n",
        "  - Evaluation: accuracy - fraction of instances predicted correctly\n",
        "  - Don't overfit: generalize by smoothing/regularizing the estimates\n",
        "- Parameter estimation: P_ML(x) = count(x)/total samples\n",
        "  - Likelihood $L(x,\\theta) = \\Pi_i P_{\\theta}(x_i)$\n",
        "  - Relative freqs are max likelihood estimates: $\\theta_{ML} argmax_{\\theta}(X_i)$\n",
        "- Laplace Smoothing: $P_{LAP,k}(x)=(c(x)+k)/(N+k|X|)$\n",
        "  - k is strength of prior\n",
        "  - For conditionals: $P_{LAP,k}(x|y)=(c(x,y)+k)/(c(y)+k|X|)$\n",
        "- Linear interpolation: $P_{LIN}(x|y)=\\alpha \\hat{P}(x|y)+(1-\\alpha)\\hat{P}(x)$\n",
        "- Hyperparamers: Amount of smoothing to do k,$\\alpha$\n",
        "  - Tune on held-out data using best value\n",
        "- Baseline: simple way to tell what \"good\" accuracy is (want better than baseline)\n",
        "- Confidence: confidence(x)=max_y P(y|x)\n",
        "  - How sure the classifier is of a classification\n",
        "\n",
        "Perceptrons\n",
        "- Linear classifiers\n",
        "  - inputs are feature values, with weights, sum is the activation\n",
        "  - activation_w(x) = w $\\cdot$ f(x) (dot product)\n",
        "- Binary Decision Rule: 1 side of vector is +1, other is -1\n",
        "- Separability: true if some parameters get training set perfectly correct\n",
        "- Convergence: converges if training is separable (binary)\n",
        "- Mistake bound: max # of mistakes (binary) related to the margin or degree of separability - mistakes < k/$\\delta^2$\n",
        "- Problems with perceptron\n",
        "  - Noise (not separable)\n",
        "  - Mediocre generalization\n",
        "  - Overtraining\n",
        "- Improving Perceptron\n",
        "  - Adjust the weight update (multiply $f(x)$ by $\\tau$)\n",
        "    - $\\tau = \\frac{(w'_y-w'_{y^*}/cdot f + 1)}{2f\\cdot f}$\n",
        "  - Maximum step size: Don't want updates to be too large so cap max step size with C\n",
        "    - $\\tau = min(\\tau, C)$\n",
        "  - Maximize the margin of the linear separator\n",
        "  - Non-linear separator\n",
        "  - Add bias term\n",
        "    - output = 0 if $w\\cdot x+b \\leq 0$, 1 otherwise\n",
        "  - Activation function: $y=a=f(z)$\n",
        "    - sigmoid, tanh (steepest), ReLU (y=0 if < 0, then y=x if >=0)\n",
        "\n",
        "Naive Bayes vs Perceptrons\n",
        "- Naive Bayes\n",
        "  - Builds a model training data\n",
        "  - Gives prediction probs\n",
        "  - Strong assumptions about feature independence\n",
        "  - One pass through the data (counting)\n",
        "- Perceptrons/MIRA\n",
        "  - Makes less assumptions about data\n",
        "  - Mistake-driven learning\n",
        "  - Multiple passes through data (prediction)\n",
        "  - Often more accurate\n",
        "\"\"\"\n",
        "\n",
        "# Definitions\n",
        "module12_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n"
      ],
      "execution_count": 124,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KUc_LgzDvWf-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 2650
        },
        "cellView": "form",
        "outputId": "8275f76f-6dfd-49d0-e32c-8623eacc047d"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module12_sections = [\n",
        "  (\"AIMA Chapter 5.1 Game Theory\", chapter19_1),\n",
        "  (\"AIMA Chapter 5.2 Optimal Decisions in Games\", chapter19_2),\n",
        "  (\"AIMA Chapter 5.3 Heuristic Alpha–Beta Tree Search\", chapter19_3),\n",
        "  (\"AIMA Chapter 5.5 Stochastic Games\", chapter19_4),\n",
        "  (\"AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\", chapter19_5),\n",
        "  (\"AIMA Chapter 16.2 The Basis of Utility Theory\", chapter19_6),\n",
        "  (\"SLP Chapter 4.1 Naive Bayes Classifiers\", slp_chapter4_1),\n",
        "  (\"SLP Chapter 4.2 Training the Naive Bayes Classifier\", slp_chapter4_2),\n",
        "  (\"SLP Chapter 4.3 Worked Example\", slp_chapter4_3),\n",
        "  (\"SLP Chapter 4.4 Optimizing for Sentiment Analysis\", slp_chapter4_4),\n",
        "  (\"SLP Chapter 4.5 Naive Bayes for other text classification tasks\", slp_chapter4_5),\n",
        "  (\"SLP Chapter 4.6 Naive Bayes as a Language Model\", slp_chapter4_6),\n",
        "  (\"SLP Chapter 4.7 Evaluation: Precision, Recall, F-measure\", slp_chapter4_7),\n",
        "  (\"SLP Chapter 4.8 Test sets and Cross-validation\", slp_chapter4_8),\n",
        "  (\"SLP Chapter 4.9 Statistical Significance Testing\", slp_chapter4_9),\n",
        "  (\"SLP Chapter 4.10 Avoiding Harms in Classification\", slp_chapter4_10),\n",
        "  (\"Module 12 Lecture Notes\", module12_lecture_notes),\n",
        "]\n",
        "\n",
        "module12_markdown = format_module(12, \"Naive Bayes and Perceptrons\", \n",
        "                         module12_sections, \n",
        "                         module12_definitions)\n",
        "display(Markdown(module12_markdown))"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 12: Naive Bayes and Perceptrons\n## AIMA Chapter 5.1 Game Theory\n Your summary here \n\n## AIMA Chapter 5.2 Optimal Decisions in Games\n Your summary here \n\n## AIMA Chapter 5.3 Heuristic Alpha–Beta Tree Search\n Your summary here \n\n## AIMA Chapter 5.5 Stochastic Games\n Your summary here \n\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n Your summary here \n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n Your summary here \n\n## SLP Chapter 4.1 Naive Bayes Classifiers\n Your summary here \n\n## SLP Chapter 4.2 Training the Naive Bayes Classifier\n Your summary here \n\n## SLP Chapter 4.3 Worked Example\n Your summary here \n\n## SLP Chapter 4.4 Optimizing for Sentiment Analysis\n Your summary here \n\n## SLP Chapter 4.5 Naive Bayes for other text classification tasks\n Your summary here \n\n## SLP Chapter 4.6 Naive Bayes as a Language Model\n Your summary here \n\n## SLP Chapter 4.7 Evaluation: Precision, Recall, F-measure\n Your summary here \n\n## SLP Chapter 4.8 Test sets and Cross-validation\n Your summary here \n\n## SLP Chapter 4.9 Statistical Significance Testing\n Your summary here \n\n## SLP Chapter 4.10 Avoiding Harms in Classification\n Your summary here \n\n## Module 12 Lecture Notes\n\n- Naitve Bayes: All features are independent effects of the label\n- General Naive Bayes: P(Y, F_1...F_n) = P(Y)$\\Pi_i$P(F_i|Y)\n- Total number of parameters is linear in nunmber of features\n- Inference for Naive Bayes\n  1. Get joint prob of label and evidence for each label - P(Y_k, f_1...f_n)\n  2. Sum to get prob of evidence - P(y_k)$\\Pi_i$P(f_i|y_k)\n  3. Normalize by dividing step 1 by step 2 - P(Y | f_1...f_n)\n- What we need in Naive Bayes\n  - Inference Method (above)\n  - Estimates of local conditional probability table $\theta$\n    - Come from training data counts\n- Important concepts\n  - Data: Training set, held out set, test set\n  - Features: attribute-value pairs which characterize each x\n  - Experimentation cycle\n    - Learn parameters on training set\n    - Tune hyperparameters on held-out set\n    - Compute accuracy of test set\n  - Evaluation: accuracy - fraction of instances predicted correctly\n  - Don't overfit: generalize by smoothing/regularizing the estimates\n- Parameter estimation: P_ML(x) = count(x)/total samples\n  - Likelihood $L(x,\theta) = \\Pi_i P_{\theta}(x_i)$\n  - Relative freqs are max likelihood estimates: $\theta_{ML} argmax_{\theta}(X_i)$\n- Laplace Smoothing: $P_{LAP,k}(x)=(c(x)+k)/(N+k|X|)$\n  - k is strength of prior\n  - For conditionals: $P_{LAP,k}(x|y)=(c(x,y)+k)/(c(y)+k|X|)$\n- Linear interpolation: $P_{LIN}(x|y)=\u0007lpha \\hat{P}(x|y)+(1-\u0007lpha)\\hat{P}(x)$\n- Hyperparamers: Amount of smoothing to do k,$\u0007lpha$\n  - Tune on held-out data using best value\n- Baseline: simple way to tell what \"good\" accuracy is (want better than baseline)\n- Confidence: confidence(x)=max_y P(y|x)\n  - How sure the classifier is of a classification\n\nPerceptrons\n- Linear classifiers\n  - inputs are feature values, with weights, sum is the activation\n  - activation_w(x) = w $\\cdot$ f(x) (dot product)\n- Binary Decision Rule: 1 side of vector is +1, other is -1\n- Separability: true if some parameters get training set perfectly correct\n- Convergence: converges if training is separable (binary)\n- Mistake bound: max # of mistakes (binary) related to the margin or degree of separability - mistakes < k/$\\delta^2$\n- Problems with perceptron\n  - Noise (not separable)\n  - Mediocre generalization\n  - Overtraining\n- Improving Perceptron\n  - Adjust the weight update (multiply $f(x)$ by $\tau$)\n    - $\tau = \frac{(w'_y-w'_{y^*}/cdot f + 1)}{2f\\cdot f}$\n  - Maximum step size: Don't want updates to be too large so cap max step size with C\n    - $\tau = min(\tau, C)$\n  - Maximize the margin of the linear separator\n  - Non-linear separator\n  - Add bias term\n    - output = 0 if $w\\cdot x+b \\leq 0$, 1 otherwise\n  - Activation function: $y=a=f(z)$\n    - sigmoid, tanh (steepest), ReLU (y=0 if < 0, then y=x if >=0)\n\nNaive Bayes vs Perceptrons\n- Naive Bayes\n  - Builds a model training data\n  - Gives prediction probs\n  - Strong assumptions about feature independence\n  - One pass through the data (counting)\n- Perceptrons/MIRA\n  - Makes less assumptions about data\n  - Mistake-driven learning\n  - Multiple passes through data (prediction)\n  - Often more accurate\n\n\n## Module 12 Definitions\n* **Concept** - definition\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qVSQhTVSyYYO"
      },
      "source": [
        "# Module 13 - Neural Networks"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wm4mfW82yaRH"
      },
      "source": [
        "# Jurafsky and Martin, Speech and Language Processing Chapter 5 “Logistic Regression” (5.1-5.6)\n",
        "\n",
        "slp_chapter5_1 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter5_2 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter5_3 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter5_4 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter5_5 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter5_6 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Jurafsky and Martin, Chapter 7 “Neural Networks and Neural Language Models”\n",
        "\n",
        "slp_chapter7_1 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter7_2 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter7_3 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter7_4 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter7_5 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter7_6 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter7_7 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Lecture notes \n",
        "module13_lecture_notes = \"\"\"\n",
        "- Classifier Components\n",
        "  1. Feature representation of the input [x1...xn]\n",
        "  2. Classification function estimates $\\hat{y}$ via p(y|x)\n",
        "  3. Objective function for learning, minimizes error on training examples\n",
        "  4. An algorithm for optimizing the objective function\n",
        "- $z = w\\cdot x + b$\n",
        "- Sigmoid: $y=1/(1+e^{-z})$\n",
        "- Probabilities: $P(y=1)=\\sigma(w\\cdot x +b)=1/(1+e^{-(w\\cdot x + b)})$\n",
        "- Decision Boundary: $\\hat{y} = $ 1 if P(y=1|x) > 0.5, 0 otherwise\n",
        "\n",
        "Learning in Logistic Regression\n",
        "  1. Objective/loss function tells us distance between system output and gold output\n",
        "    - cross entropy loss\n",
        "  2. Stochastic gradient descent alg to minimize loss function\n",
        "- Loss functions: $L(\\hat{y},y)$ like MSE\n",
        "- Cross entropy loss\n",
        "  - $L_{CE}(\\hat{y},y)= -logp(y|x) = -[ylog\\hat{y}+(1-y)log(1-\\hat{y})] -[ylog\\sigma(w\\cdot x+b) + (1-y)log(1-\\sigma(w\\cdot x+b))]$\n",
        "\n",
        "- Total loss = $-\\Sigma_{i=1}^mL_{CE}(\\hat{y}^{(i)}|y^{(i)})$\n",
        "\n",
        "- Gradient Descent $x+y \\cdot z$\n",
        "  - $\\hat{\\theta} = argmin_{\\theta} 1/m \\cdot \\Sigma_{i=1}^m L_{CE}(y^{(i)}, x^{(i)}; \\theta)$\n",
        "- Iteratively find minimum\n",
        "  - Get closer to minimum by one step of gradient descent each time\n",
        "- Update parameter with learning rate n (eta)\n",
        "  - $w^{t+1}=w^t-eta * d/dw * f(x;w)$\n",
        "    - reduce weight by learning rate times derivative of the function (slope)\n",
        "- Multiple dimensions\n",
        "  - $\\Delta_{\\theta} L(f(x;\\theta),y) =$ vector of $d/dw_i * L(f(x;\\theta),y)$\n",
        "  - $\\theta_{t+1} = \\theta_t - eta \\cdot  \\Delta L(f(x;\\theta),y)$\n",
        "  - $dL_{CE}(w,b)/dw_j=[\\sigma(w\\cdot x + b) - y]x_j$\n",
        "- Minimize avg loss\n",
        "  - $Cost(w,b)=1/m \\cdot \\Sigma_{i=1}^m L_{CE}(\\hat{y}^{(i)},y^{(i)}) = -1/m \\cdot \\Sigma_{i=1}^m y^{(i)}log \\sigma(w\\cdot x^{(i)}+b)+ (1-,y^{(i)})log (1-\\sigma(w\\cdot x^{(i}) + b))$\n",
        "  - $dCost(w,b)/dw_j= \\Sigma_{i=1}^m [\\sigma(w\\cdot x^{(i)}+b) - y^{(i)}]x_j^{(i)}$\n",
        "\n",
        "- Mini-batch training: stochastic gradient descent trains on a small batch\n",
        "- Regularization: penalize large weights with Lasso or Ridge\n",
        "- Multinomial: $softmax(z_i) = e^{z_j} / \\Sigma_{j=1}^k e^{z_j}$ $1 \\leq i \\leq k$\n",
        "\n",
        "NEURAL NETWORKS\n",
        "- Equations for feedforward network\n",
        "  1. Multiplying weight matrix by the input vector x\n",
        "  2. Adding bias vector b\n",
        "  3. applying activation function g (ie sigmoid)\n",
        "  - Output: $h = \\sigma(Wx + b)$ where W is a single matrix\n",
        "  - Output layer has weight matrix U: $z = Uh$\n",
        "  - Classify with softmax: $y = softmax(z)$\n",
        "- Training NN\n",
        "  - Loss function (cross-entropy loss)\n",
        "    - $L_{CE}(\\hat{y}, y) = - log (e^{z_j} / \\Sigma_{j=1}^K e^{z_j})$\n",
        "  - Optimization alg (gradient descent)\n",
        "    - $dLCE(w,b)/dw_j=(\\hat{y}-y)x_j=(\\sigma(w \\cdot x + b) - y)x_j$\n",
        "  - Compute the gradient of the loss function (error propagation)\n",
        "    - See paper\n",
        "\"\"\"\n",
        "\n",
        "# Definitions\n",
        "module13_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n"
      ],
      "execution_count": 126,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kKWbCsbfxL3R",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 2206
        },
        "cellView": "form",
        "outputId": "139d850c-a0e3-4893-99e0-5511edede887"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module13_sections = [\n",
        "  (\"SLP Chapter 5.1 Classification: the sigmoid\", slp_chapter5_1),\n",
        "  (\"SLP Chapter 5.2 Learning in Logistic Regression\", slp_chapter5_2),\n",
        "  (\"SLP Chapter 5.3 The cross-entropy loss function\", slp_chapter5_3),\n",
        "  (\"SLP Chapter 5.4 Gradient Descent\", slp_chapter5_4),\n",
        "  (\"SLP Chapter 5.5 Regularization\", slp_chapter5_5),\n",
        "  (\"SLP Chapter 5.6 Multinomial logistic regression\", slp_chapter5_6),\n",
        "\n",
        "  (\"SLP Chapter 7.1 Units\", slp_chapter7_1),\n",
        "  (\"SLP Chapter 7.2 The XOR problem\", slp_chapter7_2),\n",
        "  (\"SLP Chapter 7.3 Feedforward Neural Networks\", slp_chapter7_3),\n",
        "  (\"SLP Chapter 7.4 Feedforward networks for NLP: Classification\", slp_chapter7_4),\n",
        "  (\"SLP Chapter 7.5 Feedforward Neural Language Modeling\", slp_chapter7_5),\n",
        "  (\"SLP Chapter 7.6 Training Neural Nets\", slp_chapter7_6),\n",
        "  (\"SLP Chapter 7.7 Training the neural language model\", slp_chapter7_7),\n",
        "  (\"Module 13 Lecture Notes\", module13_lecture_notes),\n",
        "]\n",
        "\n",
        "module13_markdown = format_module(13, \"Neural Networks\", \n",
        "                         module13_sections, \n",
        "                         module13_definitions)\n",
        "display(Markdown(module13_markdown))"
      ],
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 13: Neural Networks\n## SLP Chapter 5.1 Classification: the sigmoid\n Your summary here \n\n## SLP Chapter 5.2 Learning in Logistic Regression\n Your summary here \n\n## SLP Chapter 5.3 The cross-entropy loss function\n Your summary here \n\n## SLP Chapter 5.4 Gradient Descent\n Your summary here \n\n## SLP Chapter 5.5 Regularization\n Your summary here \n\n## SLP Chapter 5.6 Multinomial logistic regression\n Your summary here \n\n## SLP Chapter 7.1 Units\n Your summary here \n\n## SLP Chapter 7.2 The XOR problem\n Your summary here \n\n## SLP Chapter 7.3 Feedforward Neural Networks\n Your summary here \n\n## SLP Chapter 7.4 Feedforward networks for NLP: Classification\n Your summary here \n\n## SLP Chapter 7.5 Feedforward Neural Language Modeling\n Your summary here \n\n## SLP Chapter 7.6 Training Neural Nets\n Your summary here \n\n## SLP Chapter 7.7 Training the neural language model\n Your summary here \n\n## Module 13 Lecture Notes\n\n- Classifier Components\n  1. Feature representation of the input [x1...xn]\n  2. Classification function estimates $\\hat{y}$ via p(y|x)\n  3. Objective function for learning, minimizes error on training examples\n  4. An algorithm for optimizing the objective function\n- $z = w\\cdot x + b$\n- Sigmoid: $y=1/(1+e^{-z})$\n- Probabilities: $P(y=1)=\\sigma(w\\cdot x +b)=1/(1+e^{-(w\\cdot x + b)})$\n- Decision Boundary: $\\hat{y} = $ 1 if P(y=1|x) > 0.5, 0 otherwise\n\nLearning in Logistic Regression\n  1. Objective/loss function tells us distance between system output and gold output\n    - cross entropy loss\n  2. Stochastic gradient descent alg to minimize loss function\n- Loss functions: $L(\\hat{y},y)$ like MSE\n- Cross entropy loss\n  - $L_{CE}(\\hat{y},y)= -logp(y|x) = -[ylog\\hat{y}+(1-y)log(1-\\hat{y})] -[ylog\\sigma(w\\cdot x+b) + (1-y)log(1-\\sigma(w\\cdot x+b))]$\n\n- Total loss = $-\\Sigma_{i=1}^mL_{CE}(\\hat{y}^{(i)}|y^{(i)})$\n\n- Gradient Descent $x+y \\cdot z$\n  - $\\hat{\theta} = argmin_{\theta} 1/m \\cdot \\Sigma_{i=1}^m L_{CE}(y^{(i)}, x^{(i)}; \theta)$\n- Iteratively find minimum\n  - Get closer to minimum by one step of gradient descent each time\n- Update parameter with learning rate n (eta)\n  - $w^{t+1}=w^t-eta * d/dw * f(x;w)$\n    - reduce weight by learning rate times derivative of the function (slope)\n- Multiple dimensions\n  - $\\Delta_{\theta} L(f(x;\theta),y) =$ vector of $d/dw_i * L(f(x;\theta),y)$\n  - $\theta_{t+1} = \theta_t - eta \\cdot  \\Delta L(f(x;\theta),y)$\n  - $dL_{CE}(w,b)/dw_j=[\\sigma(w\\cdot x + b) - y]x_j$\n- Minimize avg loss\n  - $Cost(w,b)=1/m \\cdot \\Sigma_{i=1}^m L_{CE}(\\hat{y}^{(i)},y^{(i)}) = -1/m \\cdot \\Sigma_{i=1}^m y^{(i)}log \\sigma(w\\cdot x^{(i)}+b)+ (1-,y^{(i)})log (1-\\sigma(w\\cdot x^{(i}) + b))$\n  - $dCost(w,b)/dw_j= \\Sigma_{i=1}^m [\\sigma(w\\cdot x^{(i)}+b) - y^{(i)}]x_j^{(i)}$\n\n- Mini-batch training: stochastic gradient descent trains on a small batch\n- Regularization: penalize large weights with Lasso or Ridge\n- Multinomial: $softmax(z_i) = e^{z_j} / \\Sigma_{j=1}^k e^{z_j}$ $1 \\leq i \\leq k$\n\nNEURAL NETWORKS\n- Equations for feedforward network\n  1. Multiplying weight matrix by the input vector x\n  2. Adding bias vector b\n  3. applying activation function g (ie sigmoid)\n  - Output: $h = \\sigma(Wx + b)$ where W is a single matrix\n  - Output layer has weight matrix U: $z = Uh$\n  - Classify with softmax: $y = softmax(z)$\n- Training NN\n  - Loss function (cross-entropy loss)\n    - $L_{CE}(\\hat{y}, y) = - log (e^{z_j} / \\Sigma_{j=1}^K e^{z_j})$\n  - Optimization alg (gradient descent)\n    - $dLCE(w,b)/dw_j=(\\hat{y}-y)x_j=(\\sigma(w \\cdot x + b) - y)x_j$\n  - Compute the gradient of the loss function (error propagation)\n    - See paper\n\n\n## Module 13 Definitions\n* **Concept** - definition\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RYESi2kMybL8"
      },
      "source": [
        "# Module 14 - Natural Language Processing"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qIRJ4YYCzNHL"
      },
      "source": [
        "# Jurafsky and Martin, Chapter 9 “Sequence Processing with Recurrent Networks” (Sections 9.1-9.3)\n",
        "\n",
        "slp_chapter9_1 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter9_2 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter9_3 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Jurafsky and Martin, Chapter 6 “Vector Semantics and Embeddings” (6.1-6.4, 6.8, 6.10-6.12)\n",
        "\n",
        "slp_chapter6_1 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter6_2 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter6_3 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter6_4 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter6_8 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter6_10 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter6_11 = \"\"\" Your summary here \"\"\"\n",
        "slp_chapter6_12 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "\n",
        "\n",
        "# Lecture notes \n",
        "module14_lecture_notes = \"\"\"\n",
        "NLP: Vector Semantics\n",
        "- Word meaning\n",
        "  - Synonym, antonym, connotations, semantic roles (buy, sell, pay of purchasing), entailment\n",
        "- Word net: complex taxonomy where each word is represented as a synset and a taxonomic hiearchy\n",
        "- Word similarity vs synonyms\n",
        "- Distributional hypothesis: relative frequency in same context -> similarity -> synonyms if a lot of similarity\n",
        "\n",
        "Word Similarity\n",
        "- Term-Document matrix\n",
        "  - term on y, doc on x\n",
        "  - cell value is # of times of occurrence in doc\n",
        "  - length of doc vectors = vocab size (usually sparse)\n",
        "  - similar documents have similar vectors (distribution of words)\n",
        "    - see paper\n",
        "- Term-Term matrix (Term-context matrix)\n",
        "  - Cell value is # of times term x appears in a context window surrounding term y\n",
        "- TF-IDF: Term freq * inverse document freq\n",
        "  - How often a word occurs in a doc / the number of docs the word is in\n",
        "  - Usually long and sparse\n",
        "- sparse vs dense vectors\n",
        "  - denser vectors are shorter, easier to use as features in ML (fewer weights), generalize better, capture synonymy better\n",
        "\n",
        "Neural Language Models\n",
        "- Language modeling: learn a function that returns the joint probability\n",
        "- NLMs vs n-gram LMs\n",
        "  1. Don't need smoothing\n",
        "  2. Handle larger histories\n",
        "  3. Generalize over contexts of similar words\n",
        "  4. Higher predictive accuracy\n",
        "  5. Slower to train\n",
        "- Bengio et al 2003\n",
        "  1. Associate each word in vocab with a vector representation (low-D)\n",
        "  2. Express the joint prob function of a word sequence in terms of the word vectors for the words in that sequence (multi-layer feed forward NN)\n",
        "  3. Simultaneously learn the word vectors and parameters of the function\n",
        "- NLMs\n",
        "  - Input: k-gram of words w_1:k\n",
        "  - Output: prob distribution over the next word\n",
        "  - $k$ context words treated as word window, each associated with embedding vector\n",
        "- Neural Probabilistic LM\n",
        "  - Seeing one of the cat/dog sentences allows them to increase the prob for that sentence & its combinatorial # of neighbor sentences in vector space\n",
        "  1. Input vectors representing identity of input word\n",
        "  2. Mapping function C from vocab item onto a low D dense vector s\n",
        "  3. R^M vector w/ m = to about 50 dimensions\n",
        "  4. Hidden layers\n",
        "  5. Predicted output word\n",
        "- Word2Vec\n",
        "  - Learn embeddings as part of word prediction process\n",
        "  - Train a classifier to predict neighboring words\n",
        "  - Positive sampling of words in context window, negative sampling of those out of context window\n",
        "  - Increase similarity between target word and positive word, decrease it between target and negative word\n",
        "- Embeddings capture relational meanings: king is to man as queen is to __? (woman)\n",
        "  - use vector arithmetic\n",
        "  - a:a* as b:b* where b* is unknown\n",
        "  - b* should be similar to b - a + a*\n",
        "- Skip-Gram Algorithm\n",
        "  1. Treat the target word and neighboring context word as positive examples\n",
        "  2. Randomly sample other words in the lexicon to get negative samples\n",
        "  3. Use logistic regression to train a classifier to distinguish those 2 cases\n",
        "  4. Use the weights as the embeddings\n",
        "  - $logP(+|t,c_{1:k}) = \\Sigma_{i=1}^k log(1/(1+e^{-t \\cdot c_i}))$\n",
        "    - dp -> prob w/ sigmoid -> independence assumption w/ log of product\n",
        "- Choosing noise words per $p_{\\alpha(w)}$\n",
        "  - $p_{\\alpha(w)} = count(w)^{\\alpha}/(\\Sigma_w count(w)^{\\alpha})$\n",
        "  - Higher $\\alpha$ means you care more about rare words and less about frequent words (\"the\")\n",
        "- Maximize $\\Sigma_{(t,c) \\in +} logP(+|t,c) + \\Sigma_{(t,c) \\in -} logP(-|t,c)$\n",
        "- Focus on one target word t\n",
        "  - $L(\\theta)= log(1/(1+e^{-t \\cdot c})) + \\Sigma_{i=1}^k log(1/1+e^{n_i \\cdot t})$\n",
        "    - Note c is context word, n is negative word\n",
        "- Evaluate embeddings\n",
        "  - correlation = [(# of concordant pairs) - (# of discordant pairs)] / total pairs\n",
        "    - total pairs = N(N-1)/2\n",
        "    - concordant pair means it agrees with human ordering, discordant pair disagrees\n",
        "      - Ex. sex, love > professor, cucumber\n",
        "- Window size C matters\n",
        "- Embeddings can help study word history\n",
        "- Embeddings represent culture and its biases\n",
        "- Embeddings = vector models of meaning\n",
        "  - more fine-grained than just a string or index\n",
        "  - Great at modeling similarity/analogy\n",
        "  - can use sparse models (tf-idf) or dense models (word2vec)\n",
        "\"\"\"\n",
        "\n",
        "# Definitions\n",
        "module14_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n"
      ],
      "execution_count": 135,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lXNcHuKjyNXa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "a0aea85f-4e34-4db9-b542-1f1111e18e35"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module14_sections = [\n",
        "  (\"SLP Chapter 9.1 Language Models Revisited\", slp_chapter9_1),\n",
        "  (\"SLP Chapter 9.2 Recurrent Neural Networks\", slp_chapter9_2),\n",
        "  (\"SLP Chapter 9.3 RNNs as Language Models\", slp_chapter9_3),\n",
        "\n",
        "  (\"SLP Chapter 6.1 Lexical Semantics\", slp_chapter6_1),\n",
        "  (\"SLP Chapter 6.2 Vector Semantics\", slp_chapter6_2),\n",
        "  (\"SLP Chapter 6.3 Words and Vectors\", slp_chapter6_3),\n",
        "  (\"SLP Chapter 6.4 Cosine for measuring similarity\", slp_chapter6_4),\n",
        "  (\"SLP Chapter 6.8 Word2vec\", slp_chapter6_8),\n",
        "  (\"SLP Chapter 6.10 Semantic properties of embeddings\", slp_chapter6_10),\n",
        "  (\"SLP Chapter 6.11 Bias and Embeddings\", slp_chapter6_11),\n",
        "  (\"SLP Chapter 6.12 Evaluating Vector Models\", slp_chapter6_12),\n",
        "  (\"Module 14 Lecture Notes\", module14_lecture_notes),\n",
        "]\n",
        "\n",
        "module14_markdown = format_module(14, \"Natural Language Processing\", \n",
        "                         module14_sections, \n",
        "                         module14_definitions)\n",
        "display(Markdown(module14_markdown))"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 14: Natural Language Processing\n## SLP Chapter 9.1 Language Models Revisited\n Your summary here \n\n## SLP Chapter 9.2 Recurrent Neural Networks\n Your summary here \n\n## SLP Chapter 9.3 RNNs as Language Models\n Your summary here \n\n## SLP Chapter 6.1 Lexical Semantics\n Your summary here \n\n## SLP Chapter 6.2 Vector Semantics\n Your summary here \n\n## SLP Chapter 6.3 Words and Vectors\n Your summary here \n\n## SLP Chapter 6.4 Cosine for measuring similarity\n Your summary here \n\n## SLP Chapter 6.8 Word2vec\n Your summary here \n\n## SLP Chapter 6.10 Semantic properties of embeddings\n Your summary here \n\n## SLP Chapter 6.11 Bias and Embeddings\n Your summary here \n\n## SLP Chapter 6.12 Evaluating Vector Models\n Your summary here \n\n## Module 14 Lecture Notes\n\nNLP: Vector Semantics\n- Word meaning\n  - Synonym, antonym, connotations, semantic roles (buy, sell, pay of purchasing), entailment\n- Word net: complex taxonomy where each word is represented as a synset and a taxonomic hiearchy\n- Word similarity vs synonyms\n- Distributional hypothesis: relative frequency in same context -> similarity -> synonyms if a lot of similarity\n\nWord Similarity\n- Term-Document matrix\n  - term on y, doc on x\n  - cell value is # of times of occurrence in doc\n  - length of doc vectors = vocab size (usually sparse)\n  - similar documents have similar vectors (distribution of words)\n    - see paper\n- Term-Term matrix (Term-context matrix)\n  - Cell value is # of times term x appears in a context window surrounding term y\n- TF-IDF: Term freq * inverse document freq\n  - How often a word occurs in a doc / the number of docs the word is in\n  - Usually long and sparse\n- sparse vs dense vectors\n  - denser vectors are shorter, easier to use as features in ML (fewer weights), generalize better, capture synonymy better\n\nNeural Language Models\n- Language modeling: learn a function that returns the joint probability\n- NLMs vs n-gram LMs\n  1. Don't need smoothing\n  2. Handle larger histories\n  3. Generalize over contexts of similar words\n  4. Higher predictive accuracy\n  5. Slower to train\n- Bengio et al 2003\n  1. Associate each word in vocab with a vector representation (low-D)\n  2. Express the joint prob function of a word sequence in terms of the word vectors for the words in that sequence (multi-layer feed forward NN)\n  3. Simultaneously learn the word vectors and parameters of the function\n- NLMs\n  - Input: k-gram of words w_1:k\n  - Output: prob distribution over the next word\n  - $k$ context words treated as word window, each associated with embedding vector\n- Neural Probabilistic LM\n  - Seeing one of the cat/dog sentences allows them to increase the prob for that sentence & its combinatorial # of neighbor sentences in vector space\n  1. Input vectors representing identity of input word\n  2. Mapping function C from vocab item onto a low D dense vector s\n  3. R^M vector w/ m = to about 50 dimensions\n  4. Hidden layers\n  5. Predicted output word\n- Word2Vec\n  - Learn embeddings as part of word prediction process\n  - Train a classifier to predict neighboring words\n  - Positive sampling of words in context window, negative sampling of those out of context window\n  - Increase similarity between target word and positive word, decrease it between target and negative word\n- Embeddings capture relational meanings: king is to man as queen is to __? (woman)\n  - use vector arithmetic\n  - a:a* as b:b* where b* is unknown\n  - b* should be similar to b - a + a*\n- Skip-Gram Algorithm\n  1. Treat the target word and neighboring context word as positive examples\n  2. Randomly sample other words in the lexicon to get negative samples\n  3. Use logistic regression to train a classifier to distinguish those 2 cases\n  4. Use the weights as the embeddings\n  - $logP(+|t,c_{1:k}) = \\Sigma_{i=1}^k log(1/(1+e^{-t \\cdot c_i}))$\n    - dp -> prob w/ sigmoid -> independence assumption w/ log of product\n- Choosing noise words per $p_{\u0007lpha(w)}$\n  - $p_{\u0007lpha(w)} = count(w)^{\u0007lpha}/(\\Sigma_w count(w)^{\u0007lpha})$\n  - Higher $\u0007lpha$ means you care more about rare words and less about frequent words (\"the\")\n- Maximize $\\Sigma_{(t,c) \\in +} logP(+|t,c) + \\Sigma_{(t,c) \\in -} logP(-|t,c)$\n- Focus on one target word t\n  - $L(\theta)= log(1/(1+e^{-t \\cdot c})) + \\Sigma_{i=1}^k log(1/1+e^{n_i \\cdot t})$\n    - Note c is context word, n is negative word\n- Evaluate embeddings\n  - correlation = [(# of concordant pairs) - (# of discordant pairs)] / total pairs\n    - total pairs = N(N-1)/2\n    - concordant pair means it agrees with human ordering, discordant pair disagrees\n      - Ex. sex, love > professor, cucumber\n- Window size C matters\n- Embeddings can help study word history\n- Embeddings represent culture and its biases\n- Embeddings = vector models of meaning\n  - more fine-grained than just a string or index\n  - Great at modeling similarity/analogy\n  - can use sparse models (tf-idf) or dense models (word2vec)\n\n\n## Module 14 Definitions\n* **Concept** - definition\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vX7lbnJd4sT5"
      },
      "source": [
        "# Your Exam Notes\n",
        "\n",
        "Here are your full set of exam notes that you can use on your midterm.  Choose **Runtime > Run all**, then your notes will be displayed.\n",
        "\n",
        "If you are taking the exam in person, then you must print a copy of your notes for yourself.   Here's how to print:\n",
        "* Run the cell below. \n",
        "* Click its \"Mirror cell in tab\" button (this is located in the upper right corner of the cell, immediately to the right of the trash can).  This will open the cell.  \n",
        "* In Chrome, you can then print your notes using the **File > Print** option from the browser's menu.  \n",
        "* In the print options, change the layout from Landscape to Portrait. \n",
        "* Clicking the Save, will save a PDF that you can then print.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "T3cm1WV542_a",
        "outputId": "c24dcd68-972d-473c-f054-d95a98a48b03"
      },
      "source": [
        "# This will generate the full set of notes that you can use for your exam.\n",
        "full_markdown = \"\\n\\n\".join([module8_markdown, \n",
        "                             module9_markdown, \n",
        "                             module10_markdown, \n",
        "                             module11_markdown, \n",
        "                             module12_markdown,\n",
        "                             module13_markdown,\n",
        "                             module14_markdown,]\n",
        "                       )\n",
        "display(Markdown(full_markdown))"
      ],
      "execution_count": 138,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 8: Markov Decision Processes\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n Chapter 16.1 summary.  $P(\\textnormal{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$ \n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n Your summary here \n\n## AIMA Chapter 16.3 Utility Functions\n Your summary here \n\n## AIMA Chapter 17.1 Sequential Decision Problems\n Your summary here \n\n## AIMA Chapter 17.2 Algorithms for MDPs\n Your summary here \n\n## Module 8 Lecture Notes\n\n- MDP is sequential decision problem, fully observable, stochastic, additive rewards\n\n- What is needed\n\n   - Set of states\n   - Set of actions\n   - Stochastic transition model\n   - Reward function\n   - Initial state\n   - Optional: terminal states\n- Performance of MDP is sum of the rewards for the transitons it takes\n- Discounting utilities: $\\Sigma_{t=0}^{inf}\\gamma^tr_t \\leq R_{max}/(1-\\gamma)$\n- $V^*(s)$ = expected utility starting in s and acting optimally\n- $Q^*(s,a)$ = expected utility starting out having raken action a from state s and then acting optimally\n- $\\pi^*(s)$ = optimal action from state s\n\n- Value iteration:\n- Start w/ V_0(s)=0 and then apply Bellman update until convergence\n- Each iteration is O(S^2A)\n- Will always converge\n- Larger discount value $\\gamma$ means it takes longer to converge\n-\n- Policy evaluation:\n- $V^{\\pi}(s)=$ expected total disconted rewards starting in s and following $\\pi$\n- Start at V_0^pi(s) = 0 and then apply Bellman update\n- Idea 1: Turn recursive Bellman equations into updates\n- Idea 2: Bellman euations are a linear system\n- O(S^2) per iteration\n\n- Policy extraction: Take argmax\n\n- Policy iteration:\n1. Policy evaluation: calculate utilities for some fixed policy until convergence\n2. Policy improvement: update policy using one-step look-ahead w/ resulting converged utilities as future values\n3. Repeat until policy converges\n\n- Utility\n- Axioms of Rationality\n1. Orderability: (A > B) V (B > A) V (A ~ B)\n2. Transitivity: (A > B) V (B > C) => (A > C)\n3. Continuity: A > B > C => there exists a p st [p,A; 1-p,C] ~ B\n4. Substitutability: A ~ B => [p,A; 1-p,C] ~ [p,B; 1-p,C]\n5. Monotonicity: A > B => (p >= q <=> [p,A; 1-p,B] >= [q,A; 1-q, B])\n- Theorem: Rational preferences imply behavior describable as maximization of expected utility\n- MEU Principle: Choose action that maximizes expected utility\n   \n\n## Module 8 Definitions\n* **Utility function** - Your definition here\n* **Expected utility** - your definition here\n* **Etc.** - your definition here\n\n\n# Module 9: Reinforcement Learning\n## AIMA Chapter 17.3 Bandit Problems\n Your summary here \n\n## AIMA Chapter 22.1 Learning from Rewards\n Your summary here \n\n## AIMA Chapter 22.2 Passive Reinforcement Learning\n Your summary here \n\n## AIMA Chapter 22.3 Active Reinforcement Learning\n Your summary here \n\n## AIMA Chapter 22.4 Generalization in Reinforcement Learning\n Your summary here \n\n## Module 9 Lecture Notes\n\n- Solving MDPs is offline planning\n- Online planning is solving as you go (learning)\n  - Exploration\n  - Exploitation\n  - Regret\n  - Sampling\n  - Difficulty\n- Reinforcement is solving an MDO when you don't know transition model T or reward function R\n\nModel-based learning:\n- Learn empirical MDP model by trying stuff out and counting outcomes s' for each s,a\n- Normalize the resulting transaction and reward for each s,a\n- Solve this MDP \n\nPassive reinforcement learning:\n- Fixed policy pi(s) and learn the state values from experience\n- Direct evaluation: Average those samples\n- Pros: easy to understand, model free, eventually computes correct avg values\n- Cons: wastes info about state connections, each state must be learned separately, long time\n- Instead, temporal difference learning: learn form every experience\n\nTemporal difference learning\n- Update V(s) for each transition we experience (s, a, s', r)\n- Move values toward value of whatever successor occurs: running avg\n  - Sample of V(s): sample = R(s,pi(s),s') + gammeV^pi(s')\n  - Update to V(s): V^pi(s) <- (1-a)V^pi(s) + alpha*sample\n  - Same update: V^pi(s) <- V^pi(s) + alpha*(sample - V^pi(s))\n- Exponential moving avg: $\bar{x}_n = (1-\u0007lpha)\bar{x}_{n-1} + \u0007lpha x_n$\n- $alpha$ is learning rate: how much you trust new observations\n- Problem: can't learn policy moves\n\nQ-Learning\n- Sample-based Q-value iteration\n  - Receive a sample (s,a,s',r)\n  - Consider your old estimate Q(s,a)\n  - Consider your new sample estimate $sample = R(s,a,s') + \\gamma max_{a'}Q(s',a')$\n  - Incorporate the new estimate into a running avg $Q(s,a) \\leftarrow (1-\u0007lpha)Q(s,a) + \u0007lpha sample$\n- Converges to optimal policy even if acting suboptimally, but\n  - Need to explore enough and make learning rate small enough (but don't decrease too quickly)\n\nExploration vs Exploitation\n- Exploration function: Takes a value estimate u and a visit count n and returns an optimistic utility\n   - Ex. f(u,n) = u + k/n\n- Modified Q-update: $Q(s,a) <-_{\u0007lpha} R(s,a,s') + \\gamma max_{a'}f(Q(s',a'), N(s',a'))$\n- Regret: Measure of total mistakes (difference between expected rewards and optimal expected rewards)\n- Minimizing regret requires optimally learning to be optimal\n- Random exploration has more regret over exploration functions\n\nApproximate Q-Learning\n- Evaluation function: ideally returns actual minimax value of the position\n- In practice: typically a weighted linear sum of features\n  - Eval(s) = w1*f1(s) + q2*f2(s) + ...wn*fn(s)\n- Use this to write a Q-function (or value function) for any state using a few weights\n  - Only an approximation\n  - Learning alg exstimates weights\n- $Q(s,a) = w_1f_1(s,a) + ... +w_nf_n(s,a)$\n- Q-learning with linear functions:\n  - transition = (s,a,r,s')\n  - difference = [r + $\\gamma max_a$ Q(s',a')] - Q(s,a) = (reward + estimate of future reward) - previous estimate of how valuable this state is\n  - $w_i = w_i + \u0007lpha (difference)f_i(s,a)\n- Essentially online OLS\n\n\n## Module 9 Definitions\n* **Term** - your definition here\n\n\n# Module 10: Probabilies and Language Models\n## AIMA Chapter 12.1 Acting under Uncertainty\n Your summary here \n\n## AIMA Chapter 12.2 Basic Probability Notation\n Your summary here \n\n## AIMA Chapter 12.3 Inference Using Full Joint Distributions\n Your summary here \n\n## AIMA Chapter 12.4 Independence\n Your summary here \n\n## AIMA Chapter 12.5 Bayes’ Rule and Its Use\n Your summary here \n\n## AIMA Chapter 12.6 Naive Bayes Models\n Your summary here \n\n## AIMA Chapter 12.7 The Wumpus World Revisited\n Your summary here \n\n## SLP Chapter 3.1 N-Grams\n Your summary here \n\n## SLP Chapter 3.2 Evaluating Language Models\n Your summary here \n\n## SLP Chapter 3.3 Sampling sentences from a language model\n Your summary here \n\n## SLP Chapter 3.4 Generalization and Zeros\n Your summary here \n\n## SLP Chapter 3.5 Smoothing\n Your summary here \n\n## SLP Chapter 3.7 Huge Language Models and Stupid Backoff\n Your summary here \n\n## Module 10 Lecture Notes\n\nProbababilitistic Inference and Rules\n- General case\n  - Evidence variables: E_1 ... E_k = e_1 ... e_k\n  - Query variable: Q\n  - Hidden variables: H_1 ... H_r\n- Want P(Q|e1...e_k)\n1. Select the entries consistent with the evidence\n2. Sum at H to get join of Query and evidene\n  - P(Q, e1...ek) = $\\Sigma_{h1,...,h_r}$P(Q,h1...hr,e1...ek)\n3. Normalize: Multiply by 1/z\n  - P(Q|e1...ek) = 1/z * P(Q, e1...ek)\n\nLanguage Models\n- Get P(w1,w2,...,wn) P(w_i | w1,...,wi-1) using chain rule\n- Maximum likelihood estimator: count and divide\n  - P(w_i | w1,...,wi-1) = count(w1,...,wi)/ count(w1,...,wi-1)\n- Markov assumption: only previous k words matter\n- n-grams\n\n\n## Module 10 Definitions\n* **Term** - your definition here\n\n\n# Module 11: Probabilistic Reasoning and Bayes’ Nets\n## AIMA Chapter 13.1 Representing Knowledge in an Uncertain Domain\n Your summary here \n\n## AIMA Chapter 13.2 The Semantics of Bayesian Networks\n Your summary here \n\n## AIMA 13.3 Exact Inference in Bayesian Networks\n Your summary here \n\n## Module 11 Lecture Notes\n\n- Bayes Nets Assumptions: P(x_i | x_1...x_i-1) = P(x_i | parents(x_i))\n- Bays Newt: technique for describing complex join distributions using simple, local distributions\n- DAG graph\n- P(x | parents(x))\n- Bayes Net = topology + local conditional probabilities\n- Size of N-node net if nodes have up to k parents = O(N*2^{k+1})\n   - Would be O(2^n) as regular joint distribution\n- (Conditional) independence? X (conditionally) independent of Y (given Z)\n  - Shade in Z (observed)\n  - Active paths\n    - Causal chain: A-> B -> C where B is unobserved (either direction)\n    - Common cause: A <- B -> C where B is unobserved\n    - Common effect (V-structure): A -> B <- C where B or one of its descendents is observed\n  - If at least one active path exists, then not independent. Else, independent.\n    - Active path is where each triple is active. If one triple along the path is inactive, then path is inactive.\n- Can run a d-separation alg to build a complete list of conidtional independences of the form X_i ind X_j | X_k1,...,X_k2\n\nInference by enumeration\n- Given evidence variables, query variable, and hidden variables, get P(Q|e1...ek)\n  1. Select entries consistent with the variables\n  2. Sum out H to get joint of query and evidence\n  3. Normalize\n- Even in Bayes' Net, this is still slow because we are recreating the joint distributions\n- NP-hard\n\n\n## Module 11 Definitions\n* **Concept** - definition\n\n\n# Module 12: Naive Bayes and Perceptrons\n## AIMA Chapter 5.1 Game Theory\n Your summary here \n\n## AIMA Chapter 5.2 Optimal Decisions in Games\n Your summary here \n\n## AIMA Chapter 5.3 Heuristic Alpha–Beta Tree Search\n Your summary here \n\n## AIMA Chapter 5.5 Stochastic Games\n Your summary here \n\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n Your summary here \n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n Your summary here \n\n## SLP Chapter 4.1 Naive Bayes Classifiers\n Your summary here \n\n## SLP Chapter 4.2 Training the Naive Bayes Classifier\n Your summary here \n\n## SLP Chapter 4.3 Worked Example\n Your summary here \n\n## SLP Chapter 4.4 Optimizing for Sentiment Analysis\n Your summary here \n\n## SLP Chapter 4.5 Naive Bayes for other text classification tasks\n Your summary here \n\n## SLP Chapter 4.6 Naive Bayes as a Language Model\n Your summary here \n\n## SLP Chapter 4.7 Evaluation: Precision, Recall, F-measure\n Your summary here \n\n## SLP Chapter 4.8 Test sets and Cross-validation\n Your summary here \n\n## SLP Chapter 4.9 Statistical Significance Testing\n Your summary here \n\n## SLP Chapter 4.10 Avoiding Harms in Classification\n Your summary here \n\n## Module 12 Lecture Notes\n\n- Naitve Bayes: All features are independent effects of the label\n- General Naive Bayes: P(Y, F_1...F_n) = P(Y)$\\Pi_i$P(F_i|Y)\n- Total number of parameters is linear in nunmber of features\n- Inference for Naive Bayes\n  1. Get joint prob of label and evidence for each label - P(Y_k, f_1...f_n)\n  2. Sum to get prob of evidence - P(y_k)$\\Pi_i$P(f_i|y_k)\n  3. Normalize by dividing step 1 by step 2 - P(Y | f_1...f_n)\n- What we need in Naive Bayes\n  - Inference Method (above)\n  - Estimates of local conditional probability table $\theta$\n    - Come from training data counts\n- Important concepts\n  - Data: Training set, held out set, test set\n  - Features: attribute-value pairs which characterize each x\n  - Experimentation cycle\n    - Learn parameters on training set\n    - Tune hyperparameters on held-out set\n    - Compute accuracy of test set\n  - Evaluation: accuracy - fraction of instances predicted correctly\n  - Don't overfit: generalize by smoothing/regularizing the estimates\n- Parameter estimation: P_ML(x) = count(x)/total samples\n  - Likelihood $L(x,\theta) = \\Pi_i P_{\theta}(x_i)$\n  - Relative freqs are max likelihood estimates: $\theta_{ML} argmax_{\theta}(X_i)$\n- Laplace Smoothing: $P_{LAP,k}(x)=(c(x)+k)/(N+k|X|)$\n  - k is strength of prior\n  - For conditionals: $P_{LAP,k}(x|y)=(c(x,y)+k)/(c(y)+k|X|)$\n- Linear interpolation: $P_{LIN}(x|y)=\u0007lpha \\hat{P}(x|y)+(1-\u0007lpha)\\hat{P}(x)$\n- Hyperparamers: Amount of smoothing to do k,$\u0007lpha$\n  - Tune on held-out data using best value\n- Baseline: simple way to tell what \"good\" accuracy is (want better than baseline)\n- Confidence: confidence(x)=max_y P(y|x)\n  - How sure the classifier is of a classification\n\nPerceptrons\n- Linear classifiers\n  - inputs are feature values, with weights, sum is the activation\n  - activation_w(x) = w $\\cdot$ f(x) (dot product)\n- Binary Decision Rule: 1 side of vector is +1, other is -1\n- Separability: true if some parameters get training set perfectly correct\n- Convergence: converges if training is separable (binary)\n- Mistake bound: max # of mistakes (binary) related to the margin or degree of separability - mistakes < k/$\\delta^2$\n- Problems with perceptron\n  - Noise (not separable)\n  - Mediocre generalization\n  - Overtraining\n- Improving Perceptron\n  - Adjust the weight update (multiply $f(x)$ by $\tau$)\n    - $\tau = \frac{(w'_y-w'_{y^*}/cdot f + 1)}{2f\\cdot f}$\n  - Maximum step size: Don't want updates to be too large so cap max step size with C\n    - $\tau = min(\tau, C)$\n  - Maximize the margin of the linear separator\n  - Non-linear separator\n  - Add bias term\n    - output = 0 if $w\\cdot x+b \\leq 0$, 1 otherwise\n  - Activation function: $y=a=f(z)$\n    - sigmoid, tanh (steepest), ReLU (y=0 if < 0, then y=x if >=0)\n\nNaive Bayes vs Perceptrons\n- Naive Bayes\n  - Builds a model training data\n  - Gives prediction probs\n  - Strong assumptions about feature independence\n  - One pass through the data (counting)\n- Perceptrons/MIRA\n  - Makes less assumptions about data\n  - Mistake-driven learning\n  - Multiple passes through data (prediction)\n  - Often more accurate\n\n\n## Module 12 Definitions\n* **Concept** - definition\n\n\n# Module 13: Neural Networks\n## SLP Chapter 5.1 Classification: the sigmoid\n Your summary here \n\n## SLP Chapter 5.2 Learning in Logistic Regression\n Your summary here \n\n## SLP Chapter 5.3 The cross-entropy loss function\n Your summary here \n\n## SLP Chapter 5.4 Gradient Descent\n Your summary here \n\n## SLP Chapter 5.5 Regularization\n Your summary here \n\n## SLP Chapter 5.6 Multinomial logistic regression\n Your summary here \n\n## SLP Chapter 7.1 Units\n Your summary here \n\n## SLP Chapter 7.2 The XOR problem\n Your summary here \n\n## SLP Chapter 7.3 Feedforward Neural Networks\n Your summary here \n\n## SLP Chapter 7.4 Feedforward networks for NLP: Classification\n Your summary here \n\n## SLP Chapter 7.5 Feedforward Neural Language Modeling\n Your summary here \n\n## SLP Chapter 7.6 Training Neural Nets\n Your summary here \n\n## SLP Chapter 7.7 Training the neural language model\n Your summary here \n\n## Module 13 Lecture Notes\n\n- Classifier Components\n  1. Feature representation of the input [x1...xn]\n  2. Classification function estimates $\\hat{y}$ via p(y|x)\n  3. Objective function for learning, minimizes error on training examples\n  4. An algorithm for optimizing the objective function\n- $z = w\\cdot x + b$\n- Sigmoid: $y=1/(1+e^{-z})$\n- Probabilities: $P(y=1)=\\sigma(w\\cdot x +b)=1/(1+e^{-(w\\cdot x + b)})$\n- Decision Boundary: $\\hat{y} = $ 1 if P(y=1|x) > 0.5, 0 otherwise\n\nLearning in Logistic Regression\n  1. Objective/loss function tells us distance between system output and gold output\n    - cross entropy loss\n  2. Stochastic gradient descent alg to minimize loss function\n- Loss functions: $L(\\hat{y},y)$ like MSE\n- Cross entropy loss\n  - $L_{CE}(\\hat{y},y)= -logp(y|x) = -[ylog\\hat{y}+(1-y)log(1-\\hat{y})] -[ylog\\sigma(w\\cdot x+b) + (1-y)log(1-\\sigma(w\\cdot x+b))]$\n\n- Total loss = $-\\Sigma_{i=1}^mL_{CE}(\\hat{y}^{(i)}|y^{(i)})$\n\n- Gradient Descent $x+y \\cdot z$\n  - $\\hat{\theta} = argmin_{\theta} 1/m \\cdot \\Sigma_{i=1}^m L_{CE}(y^{(i)}, x^{(i)}; \theta)$\n- Iteratively find minimum\n  - Get closer to minimum by one step of gradient descent each time\n- Update parameter with learning rate n (eta)\n  - $w^{t+1}=w^t-eta * d/dw * f(x;w)$\n    - reduce weight by learning rate times derivative of the function (slope)\n- Multiple dimensions\n  - $\\Delta_{\theta} L(f(x;\theta),y) =$ vector of $d/dw_i * L(f(x;\theta),y)$\n  - $\theta_{t+1} = \theta_t - eta \\cdot  \\Delta L(f(x;\theta),y)$\n  - $dL_{CE}(w,b)/dw_j=[\\sigma(w\\cdot x + b) - y]x_j$\n- Minimize avg loss\n  - $Cost(w,b)=1/m \\cdot \\Sigma_{i=1}^m L_{CE}(\\hat{y}^{(i)},y^{(i)}) = -1/m \\cdot \\Sigma_{i=1}^m y^{(i)}log \\sigma(w\\cdot x^{(i)}+b)+ (1-,y^{(i)})log (1-\\sigma(w\\cdot x^{(i}) + b))$\n  - $dCost(w,b)/dw_j= \\Sigma_{i=1}^m [\\sigma(w\\cdot x^{(i)}+b) - y^{(i)}]x_j^{(i)}$\n\n- Mini-batch training: stochastic gradient descent trains on a small batch\n- Regularization: penalize large weights with Lasso or Ridge\n- Multinomial: $softmax(z_i) = e^{z_j} / \\Sigma_{j=1}^k e^{z_j}$ $1 \\leq i \\leq k$\n\nNEURAL NETWORKS\n- Equations for feedforward network\n  1. Multiplying weight matrix by the input vector x\n  2. Adding bias vector b\n  3. applying activation function g (ie sigmoid)\n  - Output: $h = \\sigma(Wx + b)$ where W is a single matrix\n  - Output layer has weight matrix U: $z = Uh$\n  - Classify with softmax: $y = softmax(z)$\n- Training NN\n  - Loss function (cross-entropy loss)\n    - $L_{CE}(\\hat{y}, y) = - log (e^{z_j} / \\Sigma_{j=1}^K e^{z_j})$\n  - Optimization alg (gradient descent)\n    - $dLCE(w,b)/dw_j=(\\hat{y}-y)x_j=(\\sigma(w \\cdot x + b) - y)x_j$\n  - Compute the gradient of the loss function (error propagation)\n    - See paper\n\n\n## Module 13 Definitions\n* **Concept** - definition\n\n\n# Module 14: Natural Language Processing\n## SLP Chapter 9.1 Language Models Revisited\n Your summary here \n\n## SLP Chapter 9.2 Recurrent Neural Networks\n Your summary here \n\n## SLP Chapter 9.3 RNNs as Language Models\n Your summary here \n\n## SLP Chapter 6.1 Lexical Semantics\n Your summary here \n\n## SLP Chapter 6.2 Vector Semantics\n Your summary here \n\n## SLP Chapter 6.3 Words and Vectors\n Your summary here \n\n## SLP Chapter 6.4 Cosine for measuring similarity\n Your summary here \n\n## SLP Chapter 6.8 Word2vec\n Your summary here \n\n## SLP Chapter 6.10 Semantic properties of embeddings\n Your summary here \n\n## SLP Chapter 6.11 Bias and Embeddings\n Your summary here \n\n## SLP Chapter 6.12 Evaluating Vector Models\n Your summary here \n\n## Module 14 Lecture Notes\n\nNLP: Vector Semantics\n- Word meaning\n  - Synonym, antonym, connotations, semantic roles (buy, sell, pay of purchasing), entailment\n- Word net: complex taxonomy where each word is represented as a synset and a taxonomic hiearchy\n- Word similarity vs synonyms\n- Distributional hypothesis: relative frequency in same context -> similarity -> synonyms if a lot of similarity\n\nWord Similarity\n- Term-Document matrix\n  - term on y, doc on x\n  - cell value is # of times of occurrence in doc\n  - length of doc vectors = vocab size (usually sparse)\n  - similar documents have similar vectors (distribution of words)\n    - see paper\n- Term-Term matrix (Term-context matrix)\n  - Cell value is # of times term x appears in a context window surrounding term y\n- TF-IDF: Term freq * inverse document freq\n  - How often a word occurs in a doc / the number of docs the word is in\n  - Usually long and sparse\n- sparse vs dense vectors\n  - denser vectors are shorter, easier to use as features in ML (fewer weights), generalize better, capture synonymy better\n\nNeural Language Models\n- Language modeling: learn a function that returns the joint probability\n- NLMs vs n-gram LMs\n  1. Don't need smoothing\n  2. Handle larger histories\n  3. Generalize over contexts of similar words\n  4. Higher predictive accuracy\n  5. Slower to train\n- Bengio et al 2003\n  1. Associate each word in vocab with a vector representation (low-D)\n  2. Express the joint prob function of a word sequence in terms of the word vectors for the words in that sequence (multi-layer feed forward NN)\n  3. Simultaneously learn the word vectors and parameters of the function\n- NLMs\n  - Input: k-gram of words w_1:k\n  - Output: prob distribution over the next word\n  - $k$ context words treated as word window, each associated with embedding vector\n- Neural Probabilistic LM\n  - Seeing one of the cat/dog sentences allows them to increase the prob for that sentence & its combinatorial # of neighbor sentences in vector space\n  1. Input vectors representing identity of input word\n  2. Mapping function C from vocab item onto a low D dense vector s\n  3. R^M vector w/ m = to about 50 dimensions\n  4. Hidden layers\n  5. Predicted output word\n- Word2Vec\n  - Learn embeddings as part of word prediction process\n  - Train a classifier to predict neighboring words\n  - Positive sampling of words in context window, negative sampling of those out of context window\n  - Increase similarity between target word and positive word, decrease it between target and negative word\n- Embeddings capture relational meanings: king is to man as queen is to __? (woman)\n  - use vector arithmetic\n  - a:a* as b:b* where b* is unknown\n  - b* should be similar to b - a + a*\n- Skip-Gram Algorithm\n  1. Treat the target word and neighboring context word as positive examples\n  2. Randomly sample other words in the lexicon to get negative samples\n  3. Use logistic regression to train a classifier to distinguish those 2 cases\n  4. Use the weights as the embeddings\n  - $logP(+|t,c_{1:k}) = \\Sigma_{i=1}^k log(1/(1+e^{-t \\cdot c_i}))$\n    - dp -> prob w/ sigmoid -> independence assumption w/ log of product\n- Choosing noise words per $p_{\u0007lpha(w)}$\n  - $p_{\u0007lpha(w)} = count(w)^{\u0007lpha}/(\\Sigma_w count(w)^{\u0007lpha})$\n  - Higher $\u0007lpha$ means you care more about rare words and less about frequent words (\"the\")\n- Maximize $\\Sigma_{(t,c) \\in +} logP(+|t,c) + \\Sigma_{(t,c) \\in -} logP(-|t,c)$\n- Focus on one target word t\n  - $L(\theta)= log(1/(1+e^{-t \\cdot c})) + \\Sigma_{i=1}^k log(1/1+e^{n_i \\cdot t})$\n    - Note c is context word, n is negative word\n- Evaluate embeddings\n  - correlation = [(# of concordant pairs) - (# of discordant pairs)] / total pairs\n    - total pairs = N(N-1)/2\n    - concordant pair means it agrees with human ordering, discordant pair disagrees\n      - Ex. sex, love > professor, cucumber\n- Window size C matters\n- Embeddings can help study word history\n- Embeddings represent culture and its biases\n- Embeddings = vector models of meaning\n  - more fine-grained than just a string or index\n  - Great at modeling similarity/analogy\n  - can use sparse models (tf-idf) or dense models (word2vec)\n\n\n## Module 14 Definitions\n* **Concept** - definition\n",
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