Bayesian Linear Regression

Bayesian_Linear_Regression.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Bayesian Linear Regression 贝叶斯线性回归"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Name: [Your name]\n",
+    "\n",
+    "Skeleton framework for you to fill in (Code you need to provide is marked by `###`):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import scipy.io as sio\n",
+    "import numpy as np \n",
+    "from numpy.linalg import *\n",
+    "import pandas as pd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def BLR_train(Phi, y, beta=100, m_0=None, S_0=None):\n",
+    "    \"\"\"\n",
+    "    Function: Calculate the expectation and covariance of posterior distribution\n",
+    "    Input:    \n",
+    "              Phi:  Design matrix of training data, size:[number dimension]\n",
+    "              y:    Training Label, size: [number 1]\n",
+    "              beta: The precision of Gaussian random variables\n",
+    "              m_0:  The mean of conjugate prior distribution, size: [dimension 1]\n",
+    "              s_0:  The covariance of conjugate prior distribution, size: [dimension dimension]\n",
+    "    Output:   \n",
+    "              m_N:  The expectation of posterior distribution\n",
+    "              S_N:  The covariance of posterior distribution\n",
+    "    \"\"\"\n",
+    "    m, d = Phi.shape\n",
+    "    if m_0 == None:  m_0 = np.zeros((d,1))\n",
+    "    if S_0 == None: S_0 = 0.1*np.eye(d)\n",
+    "    \n",
+    "    # your code\n",
+    "    S_N = ###\n",
+    "    m_N = ###\n",
+    "    \n",
+    "    return m_N, S_N"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def BLR_test(Phi, y, m_N, S_N, beta=100):\n",
+    "    \"\"\"\n",
+    "    Function: Predict the testing data\n",
+    "    Input:\n",
+    "              Phi:  Design matrix of testing data\n",
+    "              y:    Testing Label\n",
+    "              m_N:  The expectation of posterior distribution\n",
+    "              S_N:  The covariance of posterior distribution\n",
+    "              beta: The precision of Gaussian random variables\n",
+    "    Output:\n",
+    "              t:    Prediction of testing data\n",
+    "    \"\"\"\n",
+    "    # your code\n",
+    "    mu = ###\n",
+    "    var = ###\n",
+    "    \n",
+    "    t = np.sqrt(var) * np.random.randn(y.shape[0], y.shape[1]) + mu\n",
+    "    \n",
+    "    # Three kinds of errors\n",
+    "    er = t - y\n",
+    "    MSE = (er**2).mean()                      # Mean Squared Error\n",
+    "    MAE = abs(er).mean()                      # Average Absolute Error\n",
+    "    SD = np.sqrt((( er-er.mean())**2).mean()) # Error Standard Deviation\n",
+    "    \n",
+    "    acc = np.equal(np.rint(t), y).mean() * 100\n",
+    "    text = \"The Linear Regression's accuracy is %.2f%%.\" %(acc)\n",
+    "    print(text)\n",
+    "    \n",
+    "    obj = pd.Series([MSE,MAE,SD], index=['MSE','MAE','SD'])\n",
+    "    print(obj)\n",
+    "    \n",
+    "    return t"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Import data\n",
+    "data_path = ### \"The path where you store the SpectralClassification data\" ###\n",
+    "\n",
+    "data=sio.loadmat(data_path + \"SpectralClassificationTrain.mat\") \n",
+    "train_x = data['train_x']\n",
+    "m, d = train_x.shape\n",
+    "train_x = np.column_stack( ((np.ones(m)).T , train_x) )\n",
+    "train_y = np.reshape(data['train_y'][:,0], [-1,1])\n",
+    "\n",
+    "data=sio.loadmat(data_path + \"SpectralClassificationTest.mat\") \n",
+    "test_x = data['test_x']\n",
+    "m, d = test_x.shape\n",
+    "test_x = np.column_stack( ((np.ones(m)).T , test_x) )\n",
+    "test_y = np.reshape(data['test_y'][:,0], [-1,1])\n",
+    "\n",
+    "del data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The Linear Regression's accuracy is 87.44%.\n",
+      "MSE    0.121337\n",
+      "MAE    0.291764\n",
+      "SD     0.348169\n",
+      "dtype: float64\n"
+     ]
+    }
+   ],
+   "source": [
+    "m_N, S_N = BLR_train(train_x, train_y)\n",
+    "test_t = BLR_test(train_x, train_y, m_N, S_N)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
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+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
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+   "file_extension": ".py",
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+}