{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "midterm2.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/"
        },
        "outputId": "8965b9f4-cba2-421f-83c1-e9e5c28faa2d"
      },
      "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": 40,
      "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/"
        },
        "outputId": "4ae17808-5263-4336-f55f-49e53a231aac"
      },
      "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": 41,
      "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": 42,
      "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",
        "extra_space = r\"$$$$\"\n",
        "\n",
        "a_pref_b = \"$A\\succ B$ \\t The agent prefers A over B\"\n",
        "a_indiff_b = \"$A\\sim B$ \\t The agent is indifferent between A and B\"\n",
        "a_prefeq_b = \"$A\\succeq B$ \\t The agent prefers A over B or is indifferent betwen the two\"\n",
        "\n",
        "pref = r\"$A\\succ B$\"\n",
        "pref_reverse = r\"$A\\succ B$\"\n",
        "indiff = r\"$A\\sim B$\"\n",
        "prefeq = r\"$A\\succeq B$\"\n",
        "\n",
        "transitivity_eq = r\"$A\\succ B \\and B\\succ C \\Rightarrow A\\succ C$\"\n",
        "\n",
        "orderability = r\"Orderability: \" + \"in any two lotteries, the agent must either prefer one or the other, or be indifferent, in other words, exactly one of \" + pref + \", \" + pref_reverse + \", \" + indiff + \" has to be true\"\n",
        "transitivity = r\"Transitivity: If the agent prefers $A$ to $B$, and the agent prefers $B$ to $C$, then the agent must prefer $A$ to $C$ \"\n",
        "continuity = \"\"\"Continuity: If a lottery $B$ was in between two lotteries $A, B$ in preference, there must be some probability $p$ such that the agent would be indifferent between getting $B$ for sure and\n",
        "getting a lottery that yields $A$ with probability $p$, and $B$ with probability $1 - p$\"\"\"\n",
        "substitutability = \"Substitutability: If an agent is indifferent between two lotteries $A, B$, then the agent must be indifferent between two lotteries that are identical except $A$ is substituted for $B$ or vice versa\"\n",
        "monotonicity = \"Monotonicity: If two lotteries have the same two possible outcomes ($A, B$), then if the agent prefers $A$ over $B$, the agent must prefer the lottery with the higher probability for $A$ and vice versa\"\n",
        "decomposability = \"Decomposability: Complex lotteries can be reduced to simpler ones using the laws of probability\"\n",
        "\n",
        "utility_existence = \"\"\"Existence of a Utility Function: If an agents preferences align with the Axioms of Utility Theory, then there must be some utility function $U$ such that for every $U(A), U(B)$,\n",
        "the agent prefers $A$ over $B$ if and only if $U(A) > U(B)$, and $U(A) = U(B)$ if and only if the agent is indifferent between $A, B$\"\"\"\n",
        "lottery_expectation = \"\"\"Expected Utility of a Lottery: The expected utility of a lottery is the sum of the probability of each outcome multiplied by the utility of said outcome\"\"\"\n",
        "\n",
        "chapter16_1 = \"\"\" Let's say we have an agent in an uncertain environment, to make any sort of decision in an environment where the agent is uncertain about the current state,\n",
        "the agent assigns a probability $P(s)$ to each possible current state. Let's say the agent is also uncertain about the result of its action. In order to deal with that, the agent \n",
        "assigns a probability $P(s'|s, a)$ to all possible result states $s'$ given action $a$ in state $s$. We're interested in the probability of ending up in state $s'$ if we take an action\n",
        "$a$, in order to determine that, we take the sum of probabilities for all possible sequences that would lead us to state $s'$: \"\"\"  + sample_equation + \"\"\"\\n The type of environment we use\n",
        "Markov Decision Processes is an episodic environment; one where a current action does not affect future actions. In order to decide what to do, an agent uses a utility function that expresses\n",
        "the agent's preferences. Based on that utility function, the agent uses expected utility and maximum expected utility in order to decide what to do.\"\"\"\n",
        "chapter16_2 =  \"\"\" The following notaion is used to denote the agent's preferences: \\n\"\"\" + extra_space + a_pref_b + extra_space + a_indiff_b + extra_space + a_prefeq_b + extra_space + \"\"\"We can think\n",
        "of the set of outcomes for any given action as a lottery, and of the action as the ticket. A lottery $L$ with outcomes $S_1, \\dots, S_n$ that occur with probability $p_1, \\dots, p_n$ is denoted as \\\n",
        "$$L = [p_1, S_1; \\dots; p_n, S_n;]$$ the outcome of each lottery can either be atomic or a lottery. In order to make sense of the relationship between different underlying states in a lottery, we must\n",
        "define the following constraints (Axioms of Utility Theory) for preferences between complex lotteries to make sense:\"\"\" + extra_space + orderability + extra_space + transitivity + extra_space + continuity + \"\"\"\n",
        "\"\"\" + extra_space + substitutability + extra_space + monotonicity + extra_space + decomposability + r\"$$$$\" + \"\"\"The Axioms of Utility Theory are more concerned with preferences than the utility function.\n",
        " However, from those axioms we can derive the following: \"\"\" + extra_space + utility_existence + extra_space + \"\"\"This simply implies that the utility function exists, not that it is unique\"\"\"\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 = \"\"\" Value Iteration Algorithm : takes in an MDP m with a set $S$ of states, actions $A(s)$, a transition model $P(s' | s, a)$, a reward $R(s, a, s')$, discount $\\gamma$, and maximum utility error \\epsilon.\n",
        "We also have access to $U, U'$, vectors of utilities for states in $S$, initially set to 0, and $\\delta$, the maximum change in utility to any state. We set up a loop where we initially set $U$ to $U'$ and $\\delta$ to 0. Then \n",
        "loop on all the states and we set the use the bellman equation to set $U'[s]$ (in general the equation would be expressed as $U_{i + 1}(s) = {max}_{a\\in A(s)}{\\sum_{s'}{P(s'|s, a)(R(s, a, s') + \\gamma U_i(s))}}$). Then \n",
        "if $|U'[s] - U[s]| > \\delta$, we set $\\delta$ to $|U'[s] - U[s]|$. We stop looping when $\\delta \\leq \\epsilon(1 - \\gamma)/\\gamma$.\"\"\" + extra_space + \"\"\"Policy Iteration Algorithm : The policy iteration algorithm has two steps, \n",
        "policy evaluation, and policy improvement. In the former, it takes in a policy $\\pi$ and returns a utility that such a policy would yield. In the latter, it creates a new policy that improves upon the previous one.\n",
        "The algorithm stops running when the policy utility converges. It takes in an MDP, same as value iteration, and it has a vector $U$ of utilities set to 0. It also has a vector representing the current policy. It's intially set\n",
        "to random. It initially sets the utility vector to whatever the policy evaluation algorithm returns. It creates a boolean to track whether the utility value has changed, sets it to true, and it starts looping on the states. It gets the highest q-value\n",
        "for he state, and if it's higher than the one in the current policy, it changes the current policy accordingly and sets the unchanged boolean to false. It stops looping when the boolean value indicates it's been unchanged. \n",
        "The policy evaluation step is taken by using a simplified version of the bellman equation to calculate the sum of utilities for the actions determined by the policy. The Q-Values are also calculated using the bellman equation.\"\"\"\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",
        "eu_equation = r\"\"\" $\\sum_{s'}{P(\\textnormal{RESULT}(a)=s')U(s')}$ \"\"\"\n",
        "meu_equation = r\"\"\" $\\textnormal{argmax}_{s'}{EU(a)}$ \"\"\"\n",
        "\n",
        "module8_definitions = {\n",
        "\"decision theory\" : \"choosing between alternatives based on their immediate outcomes\",\n",
        "\"utility function\" : \"assigns a number to denote how desirable the state is\",\n",
        "\"value function/ordinal utility function\" : \"a utility function that simply ranks or orders the preferences\",\n",
        "\"expected utility\" : \"average utility of all outcomes, defined by the following equation : \" + eu_equation,\n",
        "\"maximum expected utility\": meu_equation,\n",
        "\"Expected Utility of a Lottery\" : \"The expected utility of a lottery is the sum of the probability of each outcome multiplied by the utility of said outcome\",\n",
        "\"preference elicitation\" : \"the process of determining a human's utility function\",\n",
        "\"Normalized Utilities\" : \"exactly what it sounds like\",\n",
        "\"Standard Lottery\" : \"A lottery in which the alternatives are the most desirable option with probability $p$, and the least desirable option with probability $1 - p$\",\n",
        "\"value of a statistical life\" : \"a value used to estimate the approximate cost of policies and interventions\",\n",
        "\"micromort\" : \"unit of probability, equal to one in a million chance of death\",\n",
        "\"Quality Adjusted Life Year (QALY)\" : \"the approximate utility of a year's life given some circumstance affecting quality (example : undergoing chemotherapy)\",\n",
        "\"monotonic preference\" : \"if person A had a monotonic preference for item I, all other factors equal, A would always prefer a situation where I is higher/more\",\n",
        "\"expected monetary value\" : \"usually in relation to taking monetary risk, the expected value of taking said risk\",\n",
        "\"risk-averse\" : \"preference for a situation/lottery with less risk over one with more risk\",\n",
        "\"risk-seeking\" : \"preference for a situation/lottery with more risk over one with less risk\",\n",
        "\"certainty equivalent\" : \"the amount of utility that, if compared with a gamble (let's say some lottery), the person would find themselves indifferent between the alternatives\",\n",
        "\"insurance premium\" : \"expected monetary value - certainty equivalent\",\n",
        "\"risk-neutral\" : \"the lack of a particular preference for risk over certainty or vice versa\",\n",
        "\"unbiased\" : \"the expected value of error is 0\",\n",
        "\"normative theory\" : \"describes rational behavior, an ideal state\",\n",
        "\"descriptive theory\" : \"describes actual (human) behavior\",\n",
        "\"certainty effect\" : \"the phenomenon of strong preference for more certain gains\",\n",
        "\"ambiguity aversion\" : \"the phenomenon of preferring known outcomes over unknown outcomes\",\n",
        "\"framing effect\" : \"the way the problem is presented affected its perception\",\n",
        "\"anchoring effect\" : \"people's tendacy to make judgements on utility values based on relative metrics\",\n",
        "\"sequential decision problems\" : \"problems in which the next state is dependent upon the current action\",\n",
        "\"Markovian Transitions\" : \"the probability of reaching state $s'$ from state $s$ depends on $s$ only as opposed to the sequence of actions that lead to $s$\",\n",
        "\"environment history\" : \"the set of states and actions leading up to the current state\",\n",
        "\"Markov Decision Process\" : \"consists of a set of states, actions, rewards, and a transition model\",\n",
        "\"policy\" : \"solutions to MDPs, they define a set of actions based on states\",\n",
        "\"optimal policy\" : \"the policy that has the highest expected utility\",\n",
        "\"finite horizon\" : \"a time (or number of actions in a static environment) t at which to stop considering the consequences of an action\",\n",
        "\"nonstationary policy\" : \"one that takes time into account\",\n",
        "\"stationary policy\" : \"a policy in which time doesn't matter\",\n",
        "\"additive discounted rewards\" : \"utility of a set of sequences, or in other words, an environment history\",\n",
        "\"discount factor\" : \"a value between 0 and 1 determining how much the utility of a reward diminishes as a function of how far into the future it is\",\n",
        "\"purely additive rewards\" : \"when the discount factor is set to 1\",\n",
        "\"proper policy\" : \"one that eventually reaches a terminal state\",\n",
        "\"Bellman Equation\" : \"${max}_{a\\in A(s)}{\\sum_{s'}{P(s'|s, a)(R(s, a, s') + \\gamma U(s'))}}$\",\n",
        "\"action-utility function/Q-function\" : \"$Q(s, a) = \\sum_{s'}{P(s' | s, a)(R(s, a, s') + \\gamma U(s'))}$\",\n",
        "}\n",
        "\n",
        "\n"
      ],
      "execution_count": 43,
      "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": 1000
        },
        "outputId": "cfa9952d-7ba0-46f6-fa26-db1646198733"
      },
      "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": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "## WARNING: Your definition of 'discount factor' is too long!\n# Module 8: Markov Decision Processes\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n Let's say we have an agent in an uncertain environment, to make any sort of decision in an environment where the agent is uncertain about the current state,\nthe agent assigns a probability $P(s)$ to each possible current state. Let's say the agent is also uncertain about the result of its action. In order to deal with that, the agent \nassigns a probability $P(s'|s, a)$ to all possible result states $s'$ given action $a$ in state $s$. We're interested in the probability of ending up in state $s'$ if we take an action\n$a$, in order to determine that, we take the sum of probabilities for all possible sequences that would lead us to state $s'$:  $$P(\\textnormal{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$$ \n The type of environment we use\nMarkov Decision Processes is an episodic environment; one where a current action does not affect future actions. In order to decide what to do, an agent uses a utility function that expresses\nthe agent's preferences. Based on that utility function, the agent uses expected utility and maximum expected utility in order to decide what to do.\n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n The following notaion is used to denote the agent's preferences: \n$$$$$A\\succ B$ \t The agent prefers A over B$$$$$A\\sim B$ \t The agent is indifferent between A and B$$$$$A\\succeq B$ \t The agent prefers A over B or is indifferent betwen the two$$$$We can think\nof the set of outcomes for any given action as a lottery, and of the action as the ticket. A lottery $L$ with outcomes $S_1, \\dots, S_n$ that occur with probability $p_1, \\dots, p_n$ is denoted as $$L = [p_1, S_1; \\dots; p_n, S_n;]$$ the outcome of each lottery can either be atomic or a lottery. In order to make sense of the relationship between different underlying states in a lottery, we must\ndefine the following constraints (Axioms of Utility Theory) for preferences between complex lotteries to make sense:$$$$Orderability: in any two lotteries, the agent must either prefer one or the other, or be indifferent, in other words, exactly one of $A\\succ B$, $A\\succ B$, $A\\sim B$ has to be true$$$$Transitivity: If the agent prefers $A$ to $B$, and the agent prefers $B$ to $C$, then the agent must prefer $A$ to $C$ $$$$Continuity: If a lottery $B$ was in between two lotteries $A, B$ in preference, there must be some probability $p$ such that the agent would be indifferent between getting $B$ for sure and\ngetting a lottery that yields $A$ with probability $p$, and $B$ with probability $1 - p$\n$$$$Substitutability: If an agent is indifferent between two lotteries $A, B$, then the agent must be indifferent between two lotteries that are identical except $A$ is substituted for $B$ or vice versa$$$$Monotonicity: If two lotteries have the same two possible outcomes ($A, B$), then if the agent prefers $A$ over $B$, the agent must prefer the lottery with the higher probability for $A$ and vice versa$$$$Decomposability: Complex lotteries can be reduced to simpler ones using the laws of probability$$$$The Axioms of Utility Theory are more concerned with preferences than the utility function.\n However, from those axioms we can derive the following: $$$$Existence of a Utility Function: If an agents preferences align with the Axioms of Utility Theory, then there must be some utility function $U$ such that for every $U(A), U(B)$,\nthe agent prefers $A$ over $B$ if and only if $U(A) > U(B)$, and $U(A) = U(B)$ if and only if the agent is indifferent between $A, B$$$$$This simply implies that the utility function exists, not that it is unique\n\n## AIMA Chapter 16.3 Utility Functions\n Your summary here \n\n## AIMA Chapter 17.1 Sequential Decision Problems\n Your summary here \n\n## AIMA Chapter 17.2 Algorithms for MDPs\n Your summary here \n\n## Module 8 Lecture Notes\n Value Iteration Algorithm : takes in an MDP m with a set $S$ of states, actions $A(s)$, a transition model $P(s' | s, a)$, a reward $R(s, a, s')$, discount $\\gamma$, and maximum utility error \\epsilon.\nWe also have access to $U, U'$, vectors of utilities for states in $S$, initially set to 0, and $\\delta$, the maximum change in utility to any state. We set up a loop where we initially set $U$ to $U'$ and $\\delta$ to 0. Then \nloop on all the states and we set the use the bellman equation to set $U'[s]$ (in general the equation would be expressed as $U_{i + 1}(s) = {max}_{a\\in A(s)}{\\sum_{s'}{P(s'|s, a)(R(s, a, s') + \\gamma U_i(s))}}$). Then \nif $|U'[s] - U[s]| > \\delta$, we set $\\delta$ to $|U'[s] - U[s]|$. We stop looping when $\\delta \\leq \\epsilon(1 - \\gamma)/\\gamma$.$$$$Policy Iteration Algorithm : The policy iteration algorithm has two steps, \npolicy evaluation, and policy improvement. In the former, it takes in a policy $\\pi$ and returns a utility that such a policy would yield. In the latter, it creates a new policy that improves upon the previous one.\nThe algorithm stops running when the policy utility converges. It takes in an MDP, same as value iteration, and it has a vector $U$ of utilities set to 0. It also has a vector representing the current policy. It's intially set\nto random. It initially sets the utility vector to whatever the policy evaluation algorithm returns. It creates a boolean to track whether the utility value has changed, sets it to true, and it starts looping on the states. It gets the highest q-value\nfor he state, and if it's higher than the one in the current policy, it changes the current policy accordingly and sets the unchanged boolean to false. It stops looping when the boolean value indicates it's been unchanged. \nThe policy evaluation step is taken by using a simplified version of the bellman equation to calculate the sum of utilities for the actions determined by the policy. The Q-Values are also calculated using the bellman equation.\n\n## Module 8 Definitions\n* **Decision theory** - choosing between alternatives based on their immediate outcomes\n* **Utility function** - assigns a number to denote how desirable the state is\n* **Value function/ordinal utility function** - a utility function that simply ranks or orders the preferences\n* **Expected utility** - average utility of all outcomes, defined by the following equation :  $\\sum_{s'}{P(\\textnormal{RESULT}(a)=s')U(s')}$ \n* **Maximum expected utility** -  $\\textnormal{argmax}_{s'}{EU(a)}$ \n* **Expected utility of a lottery** - The expected utility of a lottery is the sum of the probability of each outcome multiplied by the utility of said outcome\n* **Preference elicitation** - the process of determining a human's utility function\n* **Normalized utilities** - exactly what it sounds like\n* **Standard lottery** - A lottery in which the alternatives are the most desirable option with probability $p$, and the least desirable option with probability $1 - p$\n* **Value of a statistical life** - a value used to estimate the approximate cost of policies and interventions\n* **Micromort** - unit of probability, equal to one in a million chance of death\n* **Quality adjusted life year (qaly)** - the approximate utility of a year's life given some circumstance affecting quality (example : undergoing chemotherapy)\n* **Monotonic preference** - if person A had a monotonic preference for item I, all other factors equal, A would always prefer a situation where I is higher/more\n* **Expected monetary value** - usually in relation to taking monetary risk, the expected value of taking said risk\n* **Risk-averse** - preference for a situation/lottery with less risk over one with more risk\n* **Risk-seeking** - preference for a situation/lottery with more risk over one with less risk\n* **Certainty equivalent** - the amount of utility that, if compared with a gamble (let's say some lottery), the person would find themselves indifferent between the alternatives\n* **Insurance premium** - expected monetary value - certainty equivalent\n* **Risk-neutral** - the lack of a particular preference for risk over certainty or vice versa\n* **Unbiased** - the expected value of error is 0\n* **Normative theory** - describes rational behavior, an ideal state\n* **Descriptive theory** - describes actual (human) behavior\n* **Certainty effect** - the phenomenon of strong preference for more certain gains\n* **Ambiguity aversion** - the phenomenon of preferring known outcomes over unknown outcomes\n* **Framing effect** - the way the problem is presented affected its perception\n* **Anchoring effect** - people's tendacy to make judgements on utility values based on relative metrics\n* **Sequential decision problems** - problems in which the next state is dependent upon the current action\n* **Markovian transitions** - the probability of reaching state $s'$ from state $s$ depends on $s$ only as opposed to the sequence of actions that lead to $s$\n* **Environment history** - the set of states and actions leading up to the current state\n* **Markov decision process** - consists of a set of states, actions, rewards, and a transition model\n* **Policy** - solutions to MDPs, they define a set of actions based on states\n* **Optimal policy** - the policy that has the highest expected utility\n* **Finite horizon** - a time (or number of actions in a static environment) t at which to stop considering the consequences of an action\n* **Nonstationary policy** - one that takes time into account\n* **Stationary policy** - a policy in which time doesn't matter\n* **Additive discounted rewards** - utility of a set of sequences, or in other words, an environment history\n* **Discount factor** - a value between 0 and 1 determining how much the utility of a reward diminishes as a function of how far into the future it is\n* **Purely additive rewards** - when the discount factor is set to 1\n* **Proper policy** - one that eventually reaches a terminal state\n* **Bellman equation** - ${max}_{a\\in A(s)}{\\sum_{s'}{P(s'|s, a)(R(s, a, s') + \\gamma U(s'))}}$\n* **Action-utility function/q-function** - $Q(s, a) = \\sum_{s'}{P(s' | s, a)(R(s, a, s') + \\gamma U(s'))}$\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 =  \"\"\" Samosa \"\"\"\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 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Each definition should be at most 25 words long.\n",
        "module9_definitions = {\n",
        "\"armed bandit\" : \"slot machine\",\n",
        "\"n-armed bandit\" : \"thought experiment, slot machine with n levers, each with some fixed unknown winning probability\",\n",
        "\"exploration\" : \"trying to gain more information about the environment taking more time to derive the probability distribution\",\n",
        "\"exploitation\" : \"using already gained knowledge to navigate the environment\",\n",
        "\"Markov Reward Process\" : \"an MDP with only one action\",\n",
        "\"Reinforcement Learning\" : \"a model of artificial intelligence that has the agent interact with the world and receive rewards based on how well its doing\",\n",
        "\"Model Based Reinforcement Learning\" : \"Using a transition model to help interpret rewards, and eventually find the MDP underlying the environment\",\n",
        "\"Model Free Reinforcement Learning\" : \"Learning how to act optimally in the environment without using or referring to an underlying model\",\n",
        "\"Action Utility Learning\" : \"Uses Q-values holding the rewards of actions in states, and bases its decisions on that\",\n",
        "\"Policy Search\" : \"Learns a policy\",\n",
        "\"Passive Reinforcement Learning\" : \"the agent's policy is fixed, and the agent simply tries to learn the utilities of different states\",\n",
        "\"Active Reinforcement Learning\" : \"the agent also has to figure out what to do instead of relying on a fixed policy\",\n",
        "\"Learning Rate\" : \"A parameter used in order to update utility functions in reinforcement learning models\",\n",
        "\"Utility function update\" : r\"$U^{\\pi}(s) = U^{\\pi}(s) + \\alpha [R(s, \\pi(s), s') + \\gamma U^{\\pi}(s') - U^{\\pi}(s)]$\"\n",
        "}"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ydOK__lwWgdp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 774
        },
        "cellView": "form",
        "outputId": "bdf580ae-f15b-440c-f1ba-731d7d69d157"
      },
      "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": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 9: Reinforcement Learning\n## AIMA Chapter 17.3 Bandit Problems\n Samosa \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 Your summary here \n\n## Module 9 Definitions\n* **Armed bandit** - slot machine\n* **N-armed bandit** - thought experiment, slot machine with n levers, each with some fixed unknown winning probability\n* **Exploration** - trying to gain more information about the environment taking more time to derive the probability distribution\n* **Exploitation** - using already gained knowledge to navigate the environment\n* **Markov reward process** - an MDP with only one action\n* **Reinforcement learning** - a model of artificial intelligence that has the agent interact with the world and receive rewards based on how well its doing\n* **Model based reinforcement learning** - Using a transition model to help interpret rewards, and eventually find the MDP underlying the environment\n* **Model free reinforcement learning** - Learning how to act optimally in the environment without using or referring to an underlying model\n* **Action utility learning** - Uses Q-values holding the rewards of actions in states, and bases its decisions on that\n* **Policy search** - Learns a policy\n* **Passive reinforcement learning** - the agent's policy is fixed, and the agent simply tries to learn the utilities of different states\n* **Active reinforcement learning** - the agent also has to figure out what to do instead of relying on a fixed policy\n* **Learning rate** - A parameter used in order to update utility functions in reinforcement learning models\n* **Utility function update** - $U^{\\pi}(s) = U^{\\pi}(s) + \\alpha [R(s, \\pi(s), s') + \\gamma U^{\\pi}(s') - U^{\\pi}(s)]$\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 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "\n",
        "# Each definition should be at most 25 words long.\n",
        "module10_definitions = {\n",
        "\"term\" : \"your definition here\",\n",
        "}"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lvtN3p7ET3Tx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "cellView": "form",
        "outputId": "6b4075d6-43e4-4a9d-d405-d1771e9494b3"
      },
      "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": 48,
      "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 Your summary here \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 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Definitions\n",
        "module11_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vqtEs0gHs9sO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "cellView": "form",
        "outputId": "663aee60-f80d-4ea0-d5a9-1213fb265563"
      },
      "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": 50,
      "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 Your summary here \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 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Definitions\n",
        "module12_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n",
        "\n"
      ],
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KUc_LgzDvWf-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "cellView": "form",
        "outputId": "d0a5a4c4-fd49-450d-ad42-d63d81c37833"
      },
      "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": 52,
      "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 Your summary here \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 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Definitions\n",
        "module13_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n"
      ],
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kKWbCsbfxL3R",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "cellView": "form",
        "outputId": "ad8585c5-ef4e-419e-92e8-daf8b35eeadf"
      },
      "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": 54,
      "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 Your summary here \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 = \"\"\" Your summary here \"\"\"\n",
        "\n",
        "# Definitions\n",
        "module14_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n",
        "\n"
      ],
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lXNcHuKjyNXa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 945
        },
        "outputId": "29cfdb0b-235d-4f46-e4c8-1dd1c100ecf5"
      },
      "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 13 Lecture Notes\", module13_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": 56,
      "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 13 Lecture Notes\n Your summary here \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": "236c8c20-18e7-447a-87d2-6d975994147e"
      },
      "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": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "## WARNING: Your definition of 'discount factor' is too long!\n# Module 8: Markov Decision Processes\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n Let's say we have an agent in an uncertain environment, to make any sort of decision in an environment where the agent is uncertain about the current state,\nthe agent assigns a probability $P(s)$ to each possible current state. Let's say the agent is also uncertain about the result of its action. In order to deal with that, the agent \nassigns a probability $P(s'|s, a)$ to all possible result states $s'$ given action $a$ in state $s$. We're interested in the probability of ending up in state $s'$ if we take an action\n$a$, in order to determine that, we take the sum of probabilities for all possible sequences that would lead us to state $s'$:  $$P(\\textnormal{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$$ \n The type of environment we use\nMarkov Decision Processes is an episodic environment; one where a current action does not affect future actions. In order to decide what to do, an agent uses a utility function that expresses\nthe agent's preferences. Based on that utility function, the agent uses expected utility and maximum expected utility in order to decide what to do.\n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n The following notaion is used to denote the agent's preferences: \n$$$$$A\\succ B$ \t The agent prefers A over B$$$$$A\\sim B$ \t The agent is indifferent between A and B$$$$$A\\succeq B$ \t The agent prefers A over B or is indifferent betwen the two$$$$We can think\nof the set of outcomes for any given action as a lottery, and of the action as the ticket. A lottery $L$ with outcomes $S_1, \\dots, S_n$ that occur with probability $p_1, \\dots, p_n$ is denoted as $$L = [p_1, S_1; \\dots; p_n, S_n;]$$ the outcome of each lottery can either be atomic or a lottery. In order to make sense of the relationship between different underlying states in a lottery, we must\ndefine the following constraints (Axioms of Utility Theory) for preferences between complex lotteries to make sense:$$$$Orderability: in any two lotteries, the agent must either prefer one or the other, or be indifferent, in other words, exactly one of $A\\succ B$, $A\\succ B$, $A\\sim B$ has to be true$$$$Transitivity: If the agent prefers $A$ to $B$, and the agent prefers $B$ to $C$, then the agent must prefer $A$ to $C$ $$$$Continuity: If a lottery $B$ was in between two lotteries $A, B$ in preference, there must be some probability $p$ such that the agent would be indifferent between getting $B$ for sure and\ngetting a lottery that yields $A$ with probability $p$, and $B$ with probability $1 - p$\n$$$$Substitutability: If an agent is indifferent between two lotteries $A, B$, then the agent must be indifferent between two lotteries that are identical except $A$ is substituted for $B$ or vice versa$$$$Monotonicity: If two lotteries have the same two possible outcomes ($A, B$), then if the agent prefers $A$ over $B$, the agent must prefer the lottery with the higher probability for $A$ and vice versa$$$$Decomposability: Complex lotteries can be reduced to simpler ones using the laws of probability$$$$The Axioms of Utility Theory are more concerned with preferences than the utility function.\n However, from those axioms we can derive the following: $$$$Existence of a Utility Function: If an agents preferences align with the Axioms of Utility Theory, then there must be some utility function $U$ such that for every $U(A), U(B)$,\nthe agent prefers $A$ over $B$ if and only if $U(A) > U(B)$, and $U(A) = U(B)$ if and only if the agent is indifferent between $A, B$$$$$This simply implies that the utility function exists, not that it is unique\n\n## AIMA Chapter 16.3 Utility Functions\n Your summary here \n\n## AIMA Chapter 17.1 Sequential Decision Problems\n Your summary here \n\n## AIMA Chapter 17.2 Algorithms for MDPs\n Your summary here \n\n## Module 8 Lecture Notes\n Value Iteration Algorithm : takes in an MDP m with a set $S$ of states, actions $A(s)$, a transition model $P(s' | s, a)$, a reward $R(s, a, s')$, discount $\\gamma$, and maximum utility error \\epsilon.\nWe also have access to $U, U'$, vectors of utilities for states in $S$, initially set to 0, and $\\delta$, the maximum change in utility to any state. We set up a loop where we initially set $U$ to $U'$ and $\\delta$ to 0. Then \nloop on all the states and we set the use the bellman equation to set $U'[s]$ (in general the equation would be expressed as $U_{i + 1}(s) = {max}_{a\\in A(s)}{\\sum_{s'}{P(s'|s, a)(R(s, a, s') + \\gamma U_i(s))}}$). Then \nif $|U'[s] - U[s]| > \\delta$, we set $\\delta$ to $|U'[s] - U[s]|$. We stop looping when $\\delta \\leq \\epsilon(1 - \\gamma)/\\gamma$.$$$$Policy Iteration Algorithm : The policy iteration algorithm has two steps, \npolicy evaluation, and policy improvement. In the former, it takes in a policy $\\pi$ and returns a utility that such a policy would yield. In the latter, it creates a new policy that improves upon the previous one.\nThe algorithm stops running when the policy utility converges. It takes in an MDP, same as value iteration, and it has a vector $U$ of utilities set to 0. It also has a vector representing the current policy. It's intially set\nto random. It initially sets the utility vector to whatever the policy evaluation algorithm returns. It creates a boolean to track whether the utility value has changed, sets it to true, and it starts looping on the states. It gets the highest q-value\nfor he state, and if it's higher than the one in the current policy, it changes the current policy accordingly and sets the unchanged boolean to false. It stops looping when the boolean value indicates it's been unchanged. \nThe policy evaluation step is taken by using a simplified version of the bellman equation to calculate the sum of utilities for the actions determined by the policy. The Q-Values are also calculated using the bellman equation.\n\n## Module 8 Definitions\n* **Decision theory** - choosing between alternatives based on their immediate outcomes\n* **Utility function** - assigns a number to denote how desirable the state is\n* **Value function/ordinal utility function** - a utility function that simply ranks or orders the preferences\n* **Expected utility** - average utility of all outcomes, defined by the following equation :  $\\sum_{s'}{P(\\textnormal{RESULT}(a)=s')U(s')}$ \n* **Maximum expected utility** -  $\\textnormal{argmax}_{s'}{EU(a)}$ \n* **Expected utility of a lottery** - The expected utility of a lottery is the sum of the probability of each outcome multiplied by the utility of said outcome\n* **Preference elicitation** - the process of determining a human's utility function\n* **Normalized utilities** - exactly what it sounds like\n* **Standard lottery** - A lottery in which the alternatives are the most desirable option with probability $p$, and the least desirable option with probability $1 - p$\n* **Value of a statistical life** - a value used to estimate the approximate cost of policies and interventions\n* **Micromort** - unit of probability, equal to one in a million chance of death\n* **Quality adjusted life year (qaly)** - the approximate utility of a year's life given some circumstance affecting quality (example : undergoing chemotherapy)\n* **Monotonic preference** - if person A had a monotonic preference for item I, all other factors equal, A would always prefer a situation where I is higher/more\n* **Expected monetary value** - usually in relation to taking monetary risk, the expected value of taking said risk\n* **Risk-averse** - preference for a situation/lottery with less risk over one with more risk\n* **Risk-seeking** - preference for a situation/lottery with more risk over one with less risk\n* **Certainty equivalent** - the amount of utility that, if compared with a gamble (let's say some lottery), the person would find themselves indifferent between the alternatives\n* **Insurance premium** - expected monetary value - certainty equivalent\n* **Risk-neutral** - the lack of a particular preference for risk over certainty or vice versa\n* **Unbiased** - the expected value of error is 0\n* **Normative theory** - describes rational behavior, an ideal state\n* **Descriptive theory** - describes actual (human) behavior\n* **Certainty effect** - the phenomenon of strong preference for more certain gains\n* **Ambiguity aversion** - the phenomenon of preferring known outcomes over unknown outcomes\n* **Framing effect** - the way the problem is presented affected its perception\n* **Anchoring effect** - people's tendacy to make judgements on utility values based on relative metrics\n* **Sequential decision problems** - problems in which the next state is dependent upon the current action\n* **Markovian transitions** - the probability of reaching state $s'$ from state $s$ depends on $s$ only as opposed to the sequence of actions that lead to $s$\n* **Environment history** - the set of states and actions leading up to the current state\n* **Markov decision process** - consists of a set of states, actions, rewards, and a transition model\n* **Policy** - solutions to MDPs, they define a set of actions based on states\n* **Optimal policy** - the policy that has the highest expected utility\n* **Finite horizon** - a time (or number of actions in a static environment) t at which to stop considering the consequences of an action\n* **Nonstationary policy** - one that takes time into account\n* **Stationary policy** - a policy in which time doesn't matter\n* **Additive discounted rewards** - utility of a set of sequences, or in other words, an environment history\n* **Discount factor** - a value between 0 and 1 determining how much the utility of a reward diminishes as a function of how far into the future it is\n* **Purely additive rewards** - when the discount factor is set to 1\n* **Proper policy** - one that eventually reaches a terminal state\n* **Bellman equation** - ${max}_{a\\in A(s)}{\\sum_{s'}{P(s'|s, a)(R(s, a, s') + \\gamma U(s'))}}$\n* **Action-utility function/q-function** - $Q(s, a) = \\sum_{s'}{P(s' | s, a)(R(s, a, s') + \\gamma U(s'))}$\n\n\n# Module 9: Reinforcement Learning\n## AIMA Chapter 17.3 Bandit Problems\n Samosa \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 Your summary here \n\n## Module 9 Definitions\n* **Armed bandit** - slot machine\n* **N-armed bandit** - thought experiment, slot machine with n levers, each with some fixed unknown winning probability\n* **Exploration** - trying to gain more information about the environment taking more time to derive the probability distribution\n* **Exploitation** - using already gained knowledge to navigate the environment\n* **Markov reward process** - an MDP with only one action\n* **Reinforcement learning** - a model of artificial intelligence that has the agent interact with the world and receive rewards based on how well its doing\n* **Model based reinforcement learning** - Using a transition model to help interpret rewards, and eventually find the MDP underlying the environment\n* **Model free reinforcement learning** - Learning how to act optimally in the environment without using or referring to an underlying model\n* **Action utility learning** - Uses Q-values holding the rewards of actions in states, and bases its decisions on that\n* **Policy search** - Learns a policy\n* **Passive reinforcement learning** - the agent's policy is fixed, and the agent simply tries to learn the utilities of different states\n* **Active reinforcement learning** - the agent also has to figure out what to do instead of relying on a fixed policy\n* **Learning rate** - A parameter used in order to update utility functions in reinforcement learning models\n* **Utility function update** - $U^{\\pi}(s) = U^{\\pi}(s) + \\alpha [R(s, \\pi(s), s') + \\gamma U^{\\pi}(s') - U^{\\pi}(s)]$\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 Your summary here \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 Your summary here \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 Your summary here \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 Your summary here \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 13 Lecture Notes\n Your summary here \n\n## Module 14 Definitions\n* **Concept** - definition\n",
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