homework1_rev2.enc

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": false,
    "nbgrader": {
     "checksum": "979b6f8823bbd681f0a04e070b770d1a",
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     "grade_id": "header",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "# Homewok 1 ML\n",
    "## Warning: \n",
    "### Don't even try to add new Import or you will marked 0 point\n",
    "### Don't make an infinite loop or you or you will marked 0 point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "#put your npm as string below\n",
    "NPM = \"1806255374\"\n",
    "\n",
    "#if someone that also take an ML class this year help you doing this assingment,put his/her NPM as list of string below\n",
    "COLLABORATORS = [\"1806169515\", \"1806255361\", \"1806255380\", \"1706005653\", \"1806255430\"]\n",
    "\n",
    "#if youre using external sources please put its link as list of string below\n",
    "SOURCES = [\"https://www.kdnuggets.com/2016/07/softmax-regression-related-logistic-regression.html\",\n",
    "          \"https://docs.scipy.org/doc/numpy/reference/generated/numpy.matrix.transpose.html\",\n",
    "           \"https://houxianxu.github.io/2015/04/23/logistic-softmax-regression/\",\n",
    "          ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "4668bf8743c05b811c5d03a5fc6115d8",
     "grade": false,
     "grade_id": "import",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from scipy.interpolate import griddata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "21a67f669f8cc8a0d97ceb97556ba2f4",
     "grade": false,
     "grade_id": "helper_func",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "def is_similar(X, Y):\n",
    "    if isinstance(X, list) and isinstance(Y, list):\n",
    "        if len(X) == len(Y):\n",
    "            return all([is_similar(x,Y[i]) for i,x in enumerate(X)])\n",
    "        else:\n",
    "            return False\n",
    "    return abs(X-Y) <= 1e-7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "40c65eee2c40c843125e2074cfbf409d",
     "grade": true,
     "grade_id": "import_check_helper",
     "locked": true,
     "points": 0,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "6e452e5999e2d507915805f16265a98d",
     "grade": false,
     "grade_id": "header_linreg",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## LINEAR REGRESSION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "f99b99903004b5eb5eb2a883dcbdc551",
     "grade": false,
     "grade_id": "hx_quest",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### score: 1 point\n",
    "without using any external library, implement h(x)\n",
    "\n",
    "$$ h(x) = \\theta^Tx $$\n",
    "\n",
    "with thetas as $\\theta$ (represented as list)\n",
    "\n",
    "x represented as list with the same length with thetas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "8bc4be778d7df98094b52982e87ab79c",
     "grade": false,
     "grade_id": "hx_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def hx(x):\n",
    "    global theta\n",
    "    # YOUR CODE HERE\n",
    "    a = len(x)\n",
    "    hx = 0\n",
    "    for i in range (a):\n",
    "        hx += theta[i]*x[i]\n",
    "    return hx\n",
    "#     raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "49cdd85e487934efc9ce8090c6cae440",
     "grade": true,
     "grade_id": "hx_test",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "theta, x = [1,2,3], [2,3,4]\n",
    "assert is_similar(hx(x),20)\n",
    "\n",
    "theta, x = [-1,-1,-1], [2,3,4]\n",
    "assert is_similar(hx(x),-9)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "809a9f446d3003ff64281be4c3892844",
     "grade": false,
     "grade_id": "JOfTheta_quest",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### score: 1 point\n",
    "\n",
    "without using any external library, using hx implemented above, implement $J(\\theta)$\n",
    "\n",
    "$$J(\\theta) = \\frac{1}{2}\\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})^2 $$\n",
    "\n",
    "y as list of target value\n",
    "\n",
    "with X as list of list of example coresponding to y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "c3d49190a179b55da2b38f719cbf1484",
     "grade": false,
     "grade_id": "JOfTheta_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def cost_func(X, y):\n",
    "    m = len(y)\n",
    "    # YOUR CODE HERE\n",
    "    cost_func = 0\n",
    "    for i in range (m):\n",
    "        cost_func += (hx(X[i])-y[i])**2\n",
    "        j = (0.5)*cost_func\n",
    "    return j\n",
    "#     raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "98d43d25d33f536e2896eff7c9d6857f",
     "grade": true,
     "grade_id": "JOfTheta_test",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "theta, X, y = [-1, 0], [[1,1],[0,1]], [-1,0]\n",
    "assert is_similar(cost_func(X,y),0)\n",
    "\n",
    "theta, X, y = [1, 1, 2], [[1,1,1],[0,0,0]], [0,0]\n",
    "assert is_similar(cost_func(X,y),8)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "b2eb755912c468c627e02840277bf59d",
     "grade": false,
     "grade_id": "sgd_quest",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### score: 1 point\n",
    "without using any external library, implement one iteration of stochastic gradient descent that use cost function above as error function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "dd2e4433daf1b56ea5a78e86e5cc11ae",
     "grade": false,
     "grade_id": "sgd_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def one_iteration_of_SGD(X, y, lr=1e-4):\n",
    "    global theta\n",
    "    alpha, m = lr, len(y)\n",
    "    for i in range(m):\n",
    "        # YOUR CODE HERE\n",
    "        error = (y[i]-hx(X[i]))\n",
    "        for j in range (len(theta)):\n",
    "            theta[j]=theta[j] + (alpha * error * X[i][j])\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "d462257663781eedb12724d22c1ec8d1",
     "grade": true,
     "grade_id": "sgd_test",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "theta, X, y = [1, 2, 1], [],[]\n",
    "# optimal theta is [0,1,-1]\n",
    "for i in range(10):\n",
    "    for j in range(10):\n",
    "        X.append([1,i,j])\n",
    "        y.append(i-j)\n",
    "theta = one_iteration_of_SGD(X, y, lr=0.02)\n",
    "assert is_similar(theta,[0.026437395230493967, 1.0273911806101215, -0.9817775908722853])\n",
    "theta = one_iteration_of_SGD(X, y, lr=0.02)\n",
    "assert is_similar(theta,[0.008423488895377855, 0.9997426554553306, -0.9996855620207235])\n",
    "theta = one_iteration_of_SGD(X, y, lr=0.02)\n",
    "assert is_similar(theta,[0.0070527414486398375, 0.9990690600988367, -1.0001740371160284])\n",
    "theta = one_iteration_of_SGD(X, y, lr=0.02)\n",
    "assert is_similar(theta,[0.006252955113893083, 0.999152947934675, -1.0001675531854075])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('cost func before', 12575.0)\n",
      "('theta(weight) before', [1, 2, 1])\n",
      "('cost func after 20 iteration', 1.0169437719700162e-05)\n",
      "('theta(weight) after 20 iteration', [0.0009404489777786889, 0.9998724942098921, -1.0000252664652551])\n",
      "\n",
      "cost/loss func plot\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1mcongratulations you have implemented linear regression from scratch \u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# PLAYGROUND\n",
    "# you can do anything here as long as not adding any new import\n",
    "\n",
    "theta, X, y = [1, 2, 1], [],[]\n",
    "# optimal theta is [0,1,-1]\n",
    "for i in range(10):\n",
    "    for j in range(10):\n",
    "        X.append([1,i,j])\n",
    "        y.append(i-j)\n",
    "\n",
    "history = []\n",
    "print('cost func before', cost_func(X,y))\n",
    "print('theta(weight) before', theta)\n",
    "for i in range(20):\n",
    "    history.append(cost_func(X,y)) \n",
    "    theta = one_iteration_of_SGD(X, y, lr=0.02)\n",
    "print('cost func after 20 iteration', cost_func(X,y))\n",
    "print('theta(weight) after 20 iteration', theta)\n",
    "\n",
    "print('\\ncost/loss func plot')\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(history)\n",
    "plt.xlabel('number of iteration')\n",
    "plt.ylabel('loss')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "print('\\033[1mcongratulations you have implemented linear regression from scratch \\033[0m')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "7d083efe63ab16adf9b1269c42140fa5",
     "grade": false,
     "grade_id": "header_glm",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "# GLM (Softmax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "cd4b53ec4de05217534f21f8de9f104a",
     "grade": false,
     "grade_id": "softmax_quest",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### score: 1 point\n",
    "without using any external library, implement a softmax function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "0f9df8ea2547434d4937effd690ffd02",
     "grade": false,
     "grade_id": "softmax_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def softmax(Z):\n",
    "    e = 2.718281828459045\n",
    "    # YOUR CODE HERE\n",
    "    d = len(Z)\n",
    "    tempz = []\n",
    "    for i in range (d):\n",
    "        expz = e**Z[i]\n",
    "        tempz.append(expz)\n",
    "        jumlah = sum(tempz)\n",
    "        \n",
    "    tempsoft = []\n",
    "    for i in (tempz):\n",
    "        softmax = i/jumlah\n",
    "        tempsoft.append(softmax)\n",
    "    return tempsoft\n",
    "#     raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "37e5e77d76a2c04e0e78a0cde1454ffb",
     "grade": true,
     "grade_id": "softmax_test",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "assert is_similar(softmax([1]), [1])\n",
    "assert is_similar(softmax([100]), [1])\n",
    "assert is_similar(softmax([0.123]), [1])\n",
    "assert is_similar(softmax([1, 1]), [0.5, 0.5])\n",
    "assert is_similar(softmax([123, 123, 123, 123]), [0.25, 0.25, 0.25, 0.25])\n",
    "assert is_similar(softmax([10, 1]), [0.9998766054240137, 0.0001233945759862318])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "668a8f05585e62c7535eb7540a3d8f01",
     "grade": false,
     "grade_id": "softmax_reg_quest",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### score: 1 point\n",
    "without using any external library, given theta/weight of a layer and x as features vector implement a single input softmax regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "e0225694db12b7cfccd4ff448d332d86",
     "grade": false,
     "grade_id": "softmax_reg_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def single_softmax_regression(x):\n",
    "    global thetas\n",
    "    # YOUR CODE HERE\n",
    "    Z = []\n",
    "    for theta in thetas:\n",
    "        hasilz=0\n",
    "        for i in range (len(theta)):\n",
    "            hasilz = hasilz + (theta[i] *x[i])\n",
    "        Z.append(hasilz)\n",
    "    return softmax(Z)\n",
    "\n",
    "def softmax_regression(X):\n",
    "    return [single_softmax_regression(x) for x in X]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "0e3d483d60b13cb44c3a215273059714",
     "grade": true,
     "grade_id": "softmax_reg_test",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "thetas = [[0,0],[0,0]]\n",
    "assert is_similar(softmax_regression([[1,0],[0,1]]),[[0.5, 0.5], [0.5, 0.5]])\n",
    "thetas = [[1,0], [0,1]]\n",
    "assert is_similar(softmax_regression([[1,0],[0,1]]),[[0.7310585786300049, 0.2689414213699951], [0.2689414213699951, 0.7310585786300049]])\n",
    "thetas = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]\n",
    "assert is_similar(softmax_regression([[1, 1, 1, 2], [1,2, 1, 3]]),[[0.25, 0.25, 0.25, 0.25], [0.25, 0.25, 0.25, 0.25]])\n",
    "thetas = [[0, 0, 0, 100], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]\n",
    "assert is_similar(softmax_regression([[1, 1, 1, 1], [0,0, 1, 0], [100,0,0,1]]),[[1, 0, 0, 0], [0.25, 0.25, 0.25, 0.25], [0.5, 0.5, 0, 0]])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "f18d0a2302f85b97237eb12de3afa62f",
     "grade": false,
     "grade_id": "softmax_predict_quest",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### score: 1 point\n",
    "without using any external library, given X as matrics of features(column) and datapoint(row) output its one hot encoded predicted class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "5e560d52d016ff93d829b69c85ee3ec8",
     "grade": false,
     "grade_id": "softmax_predict_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def predict_class(X):\n",
    "    likelyhoods = softmax_regression(X)\n",
    "    classes = [[0 for i in range(len(x))] for x in X]\n",
    "    # YOUR CODE HERE\n",
    "    for i in range (len(likelyhoods)):\n",
    "        nilaimax = max(likelyhoods[i])\n",
    "        max_index = likelyhoods[i].index(nilaimax)\n",
    "        classes[i][max_index] = 1\n",
    "    return classes\n",
    "#     raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "70a0c1c62116cbd649f59c2f79a6c26e",
     "grade": true,
     "grade_id": "softmax_predict_test",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "thetas = [[1,0], [0,1]]\n",
    "assert predict_class([[1,0],[0,1]]) == [[1, 0], [0, 1]]\n",
    "thetas = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]\n",
    "\n",
    "thetas = [[0, 0, 0, 100], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]\n",
    "assert predict_class([[1, 1, 1, 1]]) == [[1, 0, 0, 0]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "4f10dc985702ac86eef82d986168cbe1",
     "grade": true,
     "grade_id": "import_check_1",
     "locked": true,
     "points": 3,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "d36c1670517f68a39153710d68aa4d0a",
     "grade": false,
     "grade_id": "header_gda",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "# Gaussian Discriminant Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "7bec1b281bea281fc2e24b55ad1c4e6c",
     "grade": true,
     "grade_id": "import_checker_helper_1",
     "locked": true,
     "points": 0,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "e550b7767b70d29a732be7eb461bb784",
     "grade": false,
     "grade_id": "gda_quest",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### total score: 2 point\n",
    "##### 1 point for fit (correct sigma, mu0, mu1,  phi)\n",
    "##### 1 point for predict (correct compute_predict_proba_x_given_y,  compute_proba_y, predict_single)\n",
    "\n",
    "implement Gaussian Discriminant Analysis model for binary classification problem **you are only allowed to use numpy and numpy.linalg**\n",
    "\n",
    "use function fit to train the model\n",
    "\n",
    "and function predict to predict the trained model\n",
    "\n",
    "X is matrix of data (column as features, row as datapoint)\n",
    "\n",
    "y is vector of label (0 or 1) coresponding to X\n",
    "\n",
    "phi is $\\phi$\n",
    "\n",
    "mu0 is $\\mu0$\n",
    "\n",
    "mu1 is $\\mu1$\n",
    "\n",
    "sigma/covmat is $\\Sigma$\n",
    "\n",
    "### IMPLEMENTATION DETAIL\n",
    "**USE 1/(m-1) instead of 1/m for sigma/covmat or you can just use np.cov**\n",
    "\n",
    "**USE np.linalg.pinv instead of np.linalg.inv for inverse matrix (pseudo inverse instead of inverse)**\n",
    "\n",
    "**USE np.pi for pi**\n",
    "\n",
    "**USE np.det to get determinant**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "74781002ae680f61d875a27dabeda76a",
     "grade": false,
     "grade_id": "gda_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "class GDA:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.phi = None\n",
    "        self.sigma = None\n",
    "        self.mu0 = None\n",
    "        self.mu1 = None\n",
    "    \n",
    "    # update phi, sigma, mu0(mean 0), mu1(mean 1) here\n",
    "    def fit(self, X, y):\n",
    "        m = y.shape[0]\n",
    "        # YOUR CODE HERE\n",
    "        self.phi = len(y[y==1]) / m\n",
    "        self.mu0 = sum(X[y==0]) / len (y[y==0])\n",
    "        self.mu1 = sum(X[y==1]) / len (y[y==1])\n",
    "        self.sigma = (np.dot((X[y==0] - self.mu0).T,(X[y==0]-self.mu0)) + np.dot((X[y==1]-self.mu1).T,(X[y==1]-self.mu1))) / (m-1)\n",
    "#         print 'lalala'\n",
    "#         print ('self.sigma', self.sigma)\n",
    "#         raise NotImplementedError()\n",
    "        self.mus = [self.mu0, self.mu1]\n",
    "\n",
    "    \n",
    "    # return p(y)\n",
    "    def compute_proba_y(self, y):\n",
    "        # YOUR CODE HERE\n",
    "        py = self.phi**(y)*(1-self.phi)**(1-y)\n",
    "        return py\n",
    "        \n",
    "    #         raise NotImplementedError()\n",
    "    \n",
    "    # return p(x|y)\n",
    "    def compute_proba_x_given_y(self,x, y):\n",
    "        # YOUR CODE HERE\n",
    "        n = len(x)\n",
    "        pxy = 1/((2*np.pi)**(n/2) * np.linalg.det(self.sigma)**(1/2)) * np.exp(-1/2 * (x - self.mus[y]).dot(np.linalg.pinv(self.sigma)).dot((x - self.mus[y])).T)\n",
    "        return pxy\n",
    "#         raise NotImplementedError()\n",
    "\n",
    "    def predict_single(self, x):\n",
    "        proba_y0 = self.compute_proba_y(y=0)\n",
    "        proba_y1 = self.compute_proba_y(y=1)\n",
    "        \n",
    "        proba_x_given_y_0 = self.compute_proba_x_given_y(x, y=0)\n",
    "        proba_x_given_y_1 = self.compute_proba_x_given_y(x, y=1)\n",
    "        return 1 if proba_y1*proba_x_given_y_1 > proba_y0*proba_x_given_y_0 else 0\n",
    "        \n",
    "    def predict(self, X):\n",
    "        return [self.predict_single(x) for x in X]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "6543a820a015a31df675ef47ff52535f",
     "grade": true,
     "grade_id": "gda_test_fit",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lalala\n",
      "('self.sigma', array([[ 1.31469689, -0.06407885, -0.03699664],\n",
      "       [-0.06407885,  1.36877185, -0.04577584],\n",
      "       [-0.03699664, -0.04577584,  1.3349875 ]]))\n"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "\nArrays are not almost equal to 7 decimals\n ACTUAL: 0\n DESIRED: 0.5",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-118-fc3baba9e510>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     21\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgda\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtest_gda_public\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 23\u001b[1;33m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgda\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mphi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     24\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_array_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgda\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmu0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1.0170375245138221\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m0.8837860293254437\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m0.9928110497167374\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     25\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_array_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgda\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmu1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m0.982962475486178\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.1162139706745566\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m0.9928110497167374\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\python27\\lib\\site-packages\\numpy\\testing\\_private\\utils.pyc\u001b[0m in \u001b[0;36massert_almost_equal\u001b[1;34m(actual, desired, decimal, err_msg, verbose)\u001b[0m\n\u001b[0;32m    586\u001b[0m         \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    587\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdesired\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mactual\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>=\u001b[0m \u001b[1;36m1.5\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m10.0\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 588\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_build_err_msg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    589\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    590\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: \nArrays are not almost equal to 7 decimals\n ACTUAL: 0\n DESIRED: 0.5"
     ]
    }
   ],
   "source": [
    "def test_gda_public():\n",
    "    X = np.zeros((1000,3))\n",
    "    np.random.seed(103)\n",
    "    X[0:500,0] = np.random.uniform(-3,1,500)\n",
    "    np.random.seed(47)\n",
    "    X[0:500,1] = np.random.uniform(-3,1,500)\n",
    "    np.random.seed(2019)\n",
    "    X[0:500,2] = np.random.uniform(-3,1,500)\n",
    "\n",
    "    np.random.seed(103)\n",
    "    X[500:,0] = np.random.uniform(-1,3,500)\n",
    "    np.random.seed(47)\n",
    "    X[500:,1] = np.random.uniform(-1,3,500)\n",
    "    np.random.seed(2019)\n",
    "    X[500:,2] = np.random.uniform(-3,1,500)\n",
    "    y = np.array([0 if i < 500 else 1 for i in range(1000)])\n",
    "\n",
    "    gda = GDA()\n",
    "    gda.fit(X,y)\n",
    "    return X, y, gda\n",
    "\n",
    "X,y, gda = test_gda_public()\n",
    "np.testing.assert_almost_equal(gda.phi, 0.5)\n",
    "np.testing.assert_array_almost_equal(gda.mu0, [-1.0170375245138221, -0.8837860293254437, -0.9928110497167374])\n",
    "np.testing.assert_array_almost_equal(gda.mu1, [0.982962475486178, 1.1162139706745566, -0.9928110497167374])\n",
    "np.testing.assert_array_almost_equal(gda.sigma, np.array([[ 1.31469689, -0.06407885, -0.03699664], [-0.06407885,  1.36877185, -0.04577584], [-0.03699664, -0.04577584,  1.3349875 ]]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "393f2cf39cbe441f3e191fb48293b119",
     "grade": true,
     "grade_id": "gda_test_proba",
     "locked": true,
     "points": 1,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lalala\n",
      "('self.sigma', array([[ 1.31469689, -0.06407885, -0.03699664],\n",
      "       [-0.06407885,  1.36877185, -0.04577584],\n",
      "       [-0.03699664, -0.04577584,  1.3349875 ]]))\n"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "\nArrays are not almost equal to 7 decimals\n ACTUAL: 0\n DESIRED: 0.5",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-119-4b3dbca8414a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgda\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtest_gda_public\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgda\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompute_proba_y\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgda\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompute_proba_y\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\python27\\lib\\site-packages\\numpy\\testing\\_private\\utils.pyc\u001b[0m in \u001b[0;36massert_almost_equal\u001b[1;34m(actual, desired, decimal, err_msg, verbose)\u001b[0m\n\u001b[0;32m    586\u001b[0m         \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    587\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdesired\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mactual\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>=\u001b[0m \u001b[1;36m1.5\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m10.0\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 588\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_build_err_msg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    589\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    590\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: \nArrays are not almost equal to 7 decimals\n ACTUAL: 0\n DESIRED: 0.5"
     ]
    }
   ],
   "source": [
    "X,y, gda = test_gda_public()\n",
    "\n",
    "np.testing.assert_almost_equal(gda.compute_proba_y(1), 0.5)\n",
    "np.testing.assert_almost_equal(gda.compute_proba_y(0), 0.5)\n",
    "\n",
    "np.testing.assert_almost_equal(gda.compute_proba_x_given_y([-3, -3, -3], 1), 0)\n",
    "np.testing.assert_almost_equal(gda.compute_proba_x_given_y([-3, -3, -3], 0), 0.0002746507453048722)\n",
    "np.testing.assert_array_almost_equal(gda.predict([[-3,-3,-3]]), [0])\n",
    "\n",
    "np.testing.assert_almost_equal(gda.compute_proba_x_given_y([3, 3, 1], 1), 0.0003846724892885247)\n",
    "np.testing.assert_almost_equal(gda.compute_proba_x_given_y([3, 3, 1], 0), 0)\n",
    "np.testing.assert_array_almost_equal(gda.predict([[3, 3, 1]]), [1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lalala\n",
      "('self.sigma', array([[ 1.31469689, -0.06407885],\n",
      "       [-0.06407885,  1.36877185]]))\n",
      "example where GDA works well\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PLAYGROUND\n",
    "# you can do anything here as long as not adding any new import or breaking stuff\n",
    "\n",
    "X = np.zeros((1000,2))\n",
    "\n",
    "# for targe label 0\n",
    "np.random.seed(103)\n",
    "X[0:500,0] = np.random.uniform(-3,1,500)\n",
    "np.random.seed(47)\n",
    "X[0:500,1] = np.random.uniform(-3,1,500)\n",
    "\n",
    "# for targe label 1\n",
    "np.random.seed(103)\n",
    "X[500:,0] = np.random.uniform(-1,3,500)\n",
    "np.random.seed(47)\n",
    "X[500:,1] = np.random.uniform(-1,3,500)\n",
    "y = np.array([0 if i < 500 else 1 for i in range(1000)])\n",
    "\n",
    "\n",
    "gda = GDA()\n",
    "gda.fit(X,y)\n",
    "\n",
    "Z0 = [np.exp(-0.5*np.dot(np.dot((x-gda.mu0),np.linalg.pinv(gda.sigma)),(x-gda.mu0))) for x in X]\n",
    "Z1 = [np.exp(-0.5*np.dot(np.dot((x-gda.mu1),np.linalg.pinv(gda.sigma)),(x-gda.mu1))) for x in X]\n",
    "\n",
    "def plot_countour(X,Z0,Z1,y):\n",
    "    # define grid.\n",
    "    xi = np.linspace(-5,5,100)\n",
    "    yi = np.linspace(-5,5,100)\n",
    "\n",
    "    zi0 = griddata((X[:,0], X[:,1]), Z0, (xi[None,:], yi[:,None]), method='cubic')\n",
    "    zi1 = griddata((X[:,0], X[:,1]), Z1, (xi[None,:], yi[:,None]), method='cubic')    \n",
    "    plt.figure(figsize=(10,10))\n",
    "    CS = plt.contour(xi,yi,zi0,10,linewidths=0.5,colors='red')\n",
    "    CS = plt.contour(xi,yi,zi1,10,linewidths=0.5,colors='blue')\n",
    "    \n",
    "    plt.scatter(X[np.where(y==0)[0]][:,0],X[np.where(y==0)[0]][:,1],marker='o',c='red', s=1)\n",
    "    plt.scatter(X[np.where(y==1)[0]][:,0],X[np.where(y==1)[0]][:,1],marker='x',c='blue',s=1)\n",
    "    plt.xlim(-3,3)\n",
    "    plt.ylim(-3,3)\n",
    "    plt.title('gda boundary plot')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "print('example where GDA works well')\n",
    "plot_countour(X,np.array(Z0), np.array(Z1), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "578a2b5e1a398fcbc7a3a4f49ad19f40",
     "grade": true,
     "grade_id": "import_check_2",
     "locked": true,
     "points": 3,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multinomial Naive Bayes Classifier\n",
    "\n",
    "#### score 2 (you have to implement everything correctly to get 2 score, no partial scoring, you got either 2 or 0)\n",
    "implement a Multinomial Naive Bayes Classifier for text classification using laplace smoothing\n",
    "\n",
    "X is list of list of tokenized sentence\n",
    "\n",
    "y is the target label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "0cbd6908772501b19d6aded5cdc544b4",
     "grade": true,
     "grade_id": "import_check_helper_2",
     "locked": true,
     "points": 0,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "eed60034254615965d26da0743dde4f4",
     "grade": false,
     "grade_id": "mnb_ans",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "class MNB_TextClassifier:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.prior = {}\n",
    "        self.condprob = {}\n",
    "    \n",
    "    # p(class=y | {term0=x[0], term1=x[1], ...} )\n",
    "    # please note that you dont add new data to vocabulary when predicting\n",
    "    def proba_y_given_x(self, y, x):\n",
    "        # YOUR CODE HERE\n",
    "        pxy = 1\n",
    "        for word in x:\n",
    "            if word in self.condprob.keys():\n",
    "                pxy = pxy * self.condprob[word][y]\n",
    "            else:\n",
    "                pxy = pxy * self.condprob['new_word'][y]    \n",
    "        return pxy * self.proba_y(y)\n",
    "#         raise NotImplementedError()\n",
    "    \n",
    "    # p(c)\n",
    "    def proba_y(self, y):\n",
    "        return self.prior[y]\n",
    "\n",
    "    # update self.prior[class] as p(class=class) \n",
    "    # update self.condprob[term][class] as p(term=term | class=class)\n",
    "    def fit(self, X, y):\n",
    "        # YOUR CODE HERE\n",
    "        dictionary = []\n",
    "        for sentence in X:\n",
    "            dictionary  = dictionary + sentence\n",
    "        dictionary = np.unique(dictionary)\n",
    "        \n",
    "        self.prior[1] = len(y[y==1]) / len(y)\n",
    "        self.prior[0] = len(y[y==0]) / len(y)\n",
    "        \n",
    "        X1 = X[y==1]\n",
    "        X0 = X[y==0]\n",
    "        \n",
    "        for word in dictionary:\n",
    "            self.condprob[word] = {}\n",
    "            \n",
    "            #y = 1\n",
    "            numerator = 1\n",
    "            denominator1 = len(dictionary)\n",
    "            for sentence in X1:\n",
    "                numerator = numerator + sum([1 for i in sentence if i == word])\n",
    "                denominator1 = denominator1 + len(sentence)\n",
    "            self.condprob[word][1] = numerator / denominator1\n",
    "            \n",
    "            #y = 0\n",
    "            numerator = 1\n",
    "            denominator0 = len(dictionary)\n",
    "            for sentence in X0:\n",
    "                numerator = numerator + sum([1 for i in sentence if i == word])\n",
    "                denominator0 = denominator0 + len(sentence)\n",
    "            self.condprob[word][0] = numerator / denominator0\n",
    "        \n",
    "        self.condprob['new_word'] = {}\n",
    "        self.condprob['new_word'][1] = 1 / denominator1\n",
    "        self.condprob['new_word'][0] = 1 / denominator0\n",
    "#         raise NotImplementedError()\n",
    "        \n",
    "    def predict_single(self, x):\n",
    "        # YOUR CODE HERE\n",
    "        prob = self.proba_y_given_x(1,x) / (self.proba_y_given_x(1,x) + self.proba_y_given_x(0,x)) \n",
    "        if prob < 0.5:\n",
    "            y_pred = 0\n",
    "        else:\n",
    "            y_pred = 1\n",
    "        return y_pred\n",
    "#         raise NotImplementedError()\n",
    "        \n",
    "    def predict(self, X):\n",
    "        return [self.predict_single(x) for x in X]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "05e0465b7049b93df482c2fe2b246488",
     "grade": true,
     "grade_id": "mnb_test",
     "locked": true,
     "points": 2,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "ename": "AssertionError",
     "evalue": "\nArrays are not almost equal to 7 decimals\n ACTUAL: 0\n DESIRED: 0.05357142857142857",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-124-57d9870ae2b5>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     19\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mclf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcondprob\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'japan'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m9\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     20\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 21\u001b[1;33m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mclf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mproba_y_given_x\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'asdf'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.05357142857142857\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     22\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     23\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mclf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mproba_y_given_x\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'chinese'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'chinese'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'chinese'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'tokyo'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'japan'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.00030121377997263036\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\python27\\lib\\site-packages\\numpy\\testing\\_private\\utils.pyc\u001b[0m in \u001b[0;36massert_almost_equal\u001b[1;34m(actual, desired, decimal, err_msg, verbose)\u001b[0m\n\u001b[0;32m    586\u001b[0m         \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    587\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdesired\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mactual\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>=\u001b[0m \u001b[1;36m1.5\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m10.0\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 588\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_build_err_msg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    589\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    590\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: \nArrays are not almost equal to 7 decimals\n ACTUAL: 0\n DESIRED: 0.05357142857142857"
     ]
    }
   ],
   "source": [
    "X = np.array([\n",
    "    ['chinese', 'beijing', 'chinese'],\n",
    "    ['chinese', 'chinese', 'shanghai'],\n",
    "    ['chinese', 'macao'],\n",
    "    ['tokyo', 'japan', 'chinese']\n",
    "])\n",
    "\n",
    "#class 1 is china\n",
    "#class 0 is japan\n",
    "y = np.array([1,1,1,0])\n",
    "\n",
    "clf = MNB_TextClassifier()\n",
    "clf.fit(X, y)\n",
    "\n",
    "\n",
    "np.testing.assert_almost_equal(clf.condprob['chinese'][1], 3/7)\n",
    "np.testing.assert_almost_equal(clf.condprob['japan'][1], 1/14)\n",
    "np.testing.assert_almost_equal(clf.condprob['chinese'][0], 2/9)\n",
    "np.testing.assert_almost_equal(clf.condprob['japan'][0], 2/9)\n",
    "\n",
    "np.testing.assert_almost_equal(clf.proba_y_given_x(1, ['asdf']), 0.05357142857142857)\n",
    "\n",
    "np.testing.assert_almost_equal(clf.proba_y_given_x(1, ['chinese', 'chinese', 'chinese', 'tokyo', 'japan']), 0.00030121377997263036)\n",
    "np.testing.assert_almost_equal(clf.proba_y_given_x(1, ['asdfasdfasdf','asdfasdfasdf','chinese', 'chinese', 'chinese', 'tokyo', 'japan']), 1.5368049998603588e-06)\n",
    "\n",
    "np.testing.assert_almost_equal(clf.proba_y_given_x(0, ['chinese', 'chinese', 'chinese', 'tokyo', 'japan']), 0.00013548070246744226)\n",
    "\n",
    "\n",
    "np.testing.assert_almost_equal(clf.proba_y(1), 3/4)\n",
    "np.testing.assert_almost_equal(clf.proba_y(0), 1/4)\n",
    "np.testing.assert_almost_equal(clf.predict_single(['chinese', 'chinese', 'tokyo', 'japan']), 1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "6de7e48f74c582a3e3039826a29ad115",
     "grade": true,
     "grade_id": "import_check_3",
     "locked": true,
     "points": 3,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "baf2bbdb60b1df8cd6679eb4c3af1c75",
     "grade": false,
     "grade_id": "cell-f3b7ede3d1085e13",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## OPTIONAL (NO SCORE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# give us your feedback of your experience on taking this test here\n",
    "FEEDBACK = \"\""
   ]
  }
 ],
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    "name": "ipython",
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