Bernolli_Beta_Mixture_model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import beta, dirichlet\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 데이터 불러오기\n",
    "votes = pd.read_csv('./datasets/senate/votes.csv', header=None).to_numpy()\n",
    "with open('./datasets/senate/senators.txt') as f:\n",
    "    senators = [line.strip() for line in f]\n",
    "\n",
    "parties = [senator.split('(')[1][0] for senator in senators]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1, Log-Likelihood: -24615.84647041494\n",
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     ]
    }
   ],
   "source": [
    "def LogLikelihood(X, Z, theta, pi):\n",
    "    N, D = X.shape\n",
    "    K = theta.shape[0]\n",
    "    log_likelihood = 0\n",
    "    \n",
    "    for i in range(N):\n",
    "        component = Z[i]\n",
    "        log_likelihood += np.log(pi[component])\n",
    "        for d in range(D):\n",
    "            if X[i, d] != -1:  # 결측값은 무시\n",
    "                log_likelihood += X[i, d] * np.log(theta[component, d]) + (1 - X[i, d]) * np.log(1 - theta[component, d])\n",
    "    \n",
    "    return log_likelihood\n",
    "\n",
    "def GibbsSampling(X, K, alpha, beta_params, alpha_dir, num_iterations):\n",
    "    N, D = X.shape\n",
    "    Z = np.random.choice(K, N)\n",
    "    theta = np.random.beta(alpha, beta_params, (K, D))\n",
    "    pi = np.random.dirichlet(alpha_dir)\n",
    "    \n",
    "    log_likelihoods = []\n",
    "    \n",
    "    for it in range(num_iterations):\n",
    "        # Z 샘플링, Component\n",
    "        for i in range(N):\n",
    "            probs = np.array([pi[k] * np.prod([theta[k, d]**X[i, d] * (1-theta[k, d])**(1-X[i, d]) \n",
    "                                               for d in range(D) if X[i, d] != -1])\n",
    "                              for k in range(K)])\n",
    "            probs /= probs.sum()\n",
    "            Z[i] = np.random.choice(K, p=probs)\n",
    "        \n",
    "        # theta 샘플링, 성공확률(Success Probability)\n",
    "        for k in range(K):\n",
    "            for d in range(D):\n",
    "                X_kd = X[:, d][Z == k]\n",
    "                X_kd = X_kd[X_kd != -1]\n",
    "                a_post = alpha + X_kd.sum()\n",
    "                b_post = beta_params + len(X_kd) - X_kd.sum()\n",
    "                theta[k, d] = np.random.beta(a_post, b_post)\n",
    "        \n",
    "        # mixing proportions 샘플링\n",
    "        n_k = np.array([np.sum(Z == k) for k in range(K)])\n",
    "        pi = np.random.dirichlet(alpha_dir + n_k)\n",
    "        \n",
    "        # loglikelihood계산\n",
    "        log_likelihood = LogLikelihood(X, Z, theta, pi)\n",
    "        print(f\"Iteration {it + 1}, Log-Likelihood: {log_likelihood}\")\n",
    "\n",
    "        log_likelihoods.append(log_likelihood)\n",
    "    return Z, theta, pi, log_likelihoods\n",
    "\n",
    "K = 3  # Component 수\n",
    "alpha = 1  # Beta prior를 위한 하이퍼파라미터 \n",
    "beta_params = 1\n",
    "alpha_dir = np.ones(K)  # 디레클레 분포를 위한 하이퍼파라미터\n",
    "num_iterations = 200\n",
    "\n",
    "# Perform Gibbs sampling\n",
    "Z, theta, pi, log_likelihoods = GibbsSampling(votes, K, alpha, beta_params, alpha_dir, num_iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(log_likelihoods)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Log Likelihood')\n",
    "plt.title('Log Likelihood over Iterations')\n",
    "plt.show()\n",
    "\n",
    "np.save('./results/Bernolli_Beta_mixture_Z.npy', Z)\n",
    "np.save('./results/Bernolli_Beta_mixture_Z.npy', Z)\n",
    "np.save('./results/Bernolli_Beta_mixture_Z.npy', Z)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tensorflow",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}