nb04-latent-variable-models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "05080d5f-640d-4a95-bba4-f0dadda33ce5",
   "metadata": {},
   "source": [
    "# `nb04`: Latent variable models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a78222c9-7f79-4309-8c52-e94444641a17",
   "metadata": {},
   "source": [
    "<img src=\"./figures/nb06/lvm.png\" width=\"40%\" />\n",
    "\n",
    "Latent variable models (LVMs) are a class of models that are used to describe the relationship between a set of observed variables and a set of latent variables. They are used in many scientific fields to describe a data generating process and its observations. Many of the models we will discuss in this course are LVMs. In this notebook, we will showcase some of the most common LVMs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9f5bc112-332b-4db6-8aef-b9e1b129a42b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c66a8bf0",
   "metadata": {},
   "source": [
    "# Mixed membership model (LDA)\n",
    "\n",
    "<img src=\"./figures/nb06/lda.png\" width=\"60%\" /> \n",
    "\n",
    "(Reproduced from [Blei, 2011](https://www.eecis.udel.edu/~shatkay/Course/papers/UIntrotoTopicModelsBlei2011-5.pdf).)\n",
    "\n",
    "- Each topic is a distribution over words\n",
    "- Each document is a mixture of corpus-wide topics\n",
    "- Each word is drawn from one of those topics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "98585d50",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "np.random.seed(777)\n",
    "alpha = 1.0   # proportion of topics in a document\n",
    "beta = 1.0    # proportion of words in a topic\n",
    "\n",
    "K = 3  # number of topics\n",
    "V = 30 # number of words in the vocabulary\n",
    "M = 10  # number of documents\n",
    "N = 100 # number of words in a document\n",
    "\n",
    "# Latent variables\n",
    "theta_m = np.random.dirichlet([alpha]*K, M)  # proportion of topics in a document\n",
    "phi_k = np.random.dirichlet([beta]*V, K)     # proportion of words in a topic\n",
    "z_mn = np.array([[np.random.choice(K, p=theta_m[m]) for n in range(N)] for m in range(M)]) # topic of a word\n",
    "\n",
    "# Observations\n",
    "w_mn = np.array([[np.random.choice(V, p=phi_k[z_mn[m, n]]) for n in range(N)] for m in range(M)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5e7a1794",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1000x500 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.subplots_adjust(wspace=0.5, hspace=0.5)\n",
    "\n",
    "for m in range(M):\n",
    "    plt.subplot(2, 5, m+1)\n",
    "    plt.bar(range(K), theta_m[m], tick_label=range(K))\n",
    "    plt.xlabel('Topic')\n",
    "    plt.ylabel('Probability')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "\n",
    "for k in range(K):\n",
    "    plt.subplot(1, 3, k+1)\n",
    "    plt.bar(range(V), phi_k[k], tick_label=range(V))\n",
    "    plt.xlabel('Word')\n",
    "    plt.ylabel('Probability')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.imshow(z_mn, cmap='gray', aspect='auto')\n",
    "plt.title('Document-topic assignment')\n",
    "plt.xlabel('Word')\n",
    "plt.ylabel('Document')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.imshow(w_mn, cmap='gray', aspect='auto')\n",
    "plt.title('Word')\n",
    "plt.xlabel('Word')\n",
    "plt.ylabel('Document')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91248cab",
   "metadata": {},
   "source": [
    "<img src=\"./figures/nb06/lda-results.png\" width=\"60%\" /> "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dats0001",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}