{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.176669Z",
     "iopub.status.busy": "2025-09-11T15:37:23.176540Z",
     "iopub.status.idle": "2025-09-11T15:37:23.586259Z",
     "shell.execute_reply": "2025-09-11T15:37:23.586020Z"
    }
   },
   "outputs": [],
   "source": [
    "# Import necessary libraries\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "# Load test module for sanity check\n",
    "from test_utils import test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TYyZPqnPmhYC"
   },
   "source": [
    "Data Generation\n",
    "==="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.587686Z",
     "iopub.status.busy": "2025-09-11T15:37:23.587576Z",
     "iopub.status.idle": "2025-09-11T15:37:23.601092Z",
     "shell.execute_reply": "2025-09-11T15:37:23.600852Z"
    }
   },
   "outputs": [],
   "source": [
    "from numpy.random import rand, randn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.602156Z",
     "iopub.status.busy": "2025-09-11T15:37:23.602083Z",
     "iopub.status.idle": "2025-09-11T15:37:23.612574Z",
     "shell.execute_reply": "2025-09-11T15:37:23.612368Z"
    }
   },
   "outputs": [],
   "source": [
    "n, d, k = 100, 2, 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.613672Z",
     "iopub.status.busy": "2025-09-11T15:37:23.613606Z",
     "iopub.status.idle": "2025-09-11T15:37:23.625922Z",
     "shell.execute_reply": "2025-09-11T15:37:23.625727Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([0.69872366, 0.75176984]), array([0.25997411, 0.14504062])]\n",
      "[array([[0.01764816, 0.        ],\n",
      "       [0.        , 0.06360523]]), array([[0.01764816, 0.        ],\n",
      "       [0.        , 0.06360523]])]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(20)\n",
    "X = rand(n, d)\n",
    "\n",
    "# means = [rand(d)  for _ in range(k)]  # works for any k\n",
    "means = [rand(d) * 0.5 + 0.5, -rand(d) * 0.5 + 0.5]  # for better plotting when k = 2\n",
    "\n",
    "S = np.diag(rand(d))\n",
    "\n",
    "sigmas = [S] * k  # we'll use the same Sigma for all clusters for better visual results\n",
    "\n",
    "print(means)\n",
    "print(sigmas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the probability density"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recall the math\n",
    "\n",
    "For each data point $x_i$, the Gaussian exponent needs\n",
    "\n",
    "$$\n",
    "Q_i \\;=\\; (x_i - \\mu)^\\top \\Sigma^{-1} (x_i - \\mu).\n",
    "$$\n",
    "\n",
    "Let\n",
    "\n",
    "- $Y = X - \\mu$  (shape $n \\times d$)  \n",
    "- $A = \\Sigma^{-1}$  (shape $d \\times d$)  \n",
    "\n",
    "so that\n",
    "\n",
    "$$\n",
    "Q_i = Y_i^\\top A Y_i.\n",
    "$$\n",
    "\n",
    "where $Y_i$ is the feature vector of data point $i$.\n",
    "\n",
    "How can we get $Q_i$?\n",
    "\n",
    "Option 1: $YA$ is of shape $(n,d)$ and $Y$ is of shape $(n,d)$. Elementwise multiplication gives $(n,d)$, and row sum is the scalar quadratic form.\n",
    "\n",
    "$$\n",
    "\\sum_{k=1}^d Y_{ik}(Y_iA)_k = Y_i^\\top A Y_i\n",
    "$$\n",
    "\n",
    "Option 2: Take the diagonal entries of the gram matrix:\n",
    "$$\n",
    "[((YA)Y^\\top)]_{ii} = (Y_iA)\\cdot Y = Y_i^\\top AY_i\n",
    "$$\n",
    "\n",
    "Option 3:\n",
    "Iterate each data point and calculate point-wise $Q_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.641792Z",
     "iopub.status.busy": "2025-09-11T15:37:23.641687Z",
     "iopub.status.idle": "2025-09-11T15:37:23.659293Z",
     "shell.execute_reply": "2025-09-11T15:37:23.659066Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Your `compute_p` passed 1 tests.\n"
     ]
    }
   ],
   "source": [
    "def compute_p(X, mean, sigma):\n",
    "    \"\"\"\n",
    "    Compute the probability of each data point in X under a Gaussian distribution\n",
    "\n",
    "    Args:\n",
    "        X: (n, d) numpy array, where each row corresponds to a data point\n",
    "        mean: (d, ) numpy array, the mean of the Gaussian distribution\n",
    "        sigma: (d, d) numpy array, the covariance matrix of the Gaussian distribution\n",
    "\n",
    "    Returns:\n",
    "        p: (n, ) numpy array, the probability of each data point\n",
    "\n",
    "    >>> compute_p(np.array([[0, 0], [1, 1]]), np.array([0, 0]), np.eye(2))\n",
    "    array([0.15915494, 0.05854983])\n",
    "    \"\"\"\n",
    "\n",
    "    d = X.shape[1]\n",
    "    dxm = X - mean\n",
    "    const = 1 / np.sqrt((2 * np.pi) ** d * np.linalg.det(sigma))\n",
    "\n",
    "    ###############################\n",
    "    # Option 1: elementwise (Hadamard) multiplication via * operation\n",
    "    ###############################\n",
    "    \"\"\"\n",
    "    np.dot(dxm, np.linalg.inv(sigma) gives a matrix of shape (n,d)\n",
    "    dxm is of shape (n,d)\n",
    "    * is elementwise (Hadamard) multiplication, which gives elementwise multiplication\n",
    "    so dxm * np.dot(dxm, np.linalg.inv(sigma)) is a (n,d) matrix,\n",
    "    with each \n",
    "    \"\"\"\n",
    "    # exponent = -0.5 * np.sum(dxm * np.dot(dxm, np.linalg.inv(sigma)), axis=1)\n",
    "\n",
    "    ###############################\n",
    "    # Option 2: matrix multiplication\n",
    "    ###############################\n",
    "    \"\"\"\n",
    "    Note after matrix multiplication, we have a gram matrix of shape (n,n)\n",
    "    we only need the diagonal entries \n",
    "    \"\"\"\n",
    "    # 1) using np.dot or dot()\n",
    "    # exponent = -0.5 * (np.dot(np.dot(dxm, np.linalg.inv(sigma)), dxm.transpose())).diagonal()\n",
    "    # equivalently,\n",
    "    # exponent = -0.5 * (dxm.dot(np.linalg.inv(sigma)).dot(dxm.transpose())).diagonal()\n",
    "    # 2) using @ operator\n",
    "    exponent = -0.5 * ((dxm @ np.linalg.inv(sigma)) @ dxm.transpose()).diagonal()\n",
    "    return const * np.exp(exponent)\n",
    "\n",
    "    ###############################\n",
    "    # Option 3: iteration through all data points\n",
    "    ###############################\n",
    "    # [n, d] = np.shape(X)\n",
    "    # invSigma = np.linalg.inv(sigma)\n",
    "\n",
    "    # result = np.zeros((n,))\n",
    "    # for i in range(n):\n",
    "    #     xmu = X[i] - mean # shape (d,)\n",
    "    #     result[i] = const * np.exp(-0.5 * (xmu).T.dot(invSigma).dot(xmu))\n",
    "    # return result\n",
    "\n",
    "    ### TEMPLATE\n",
    "    # # ***************************************************\n",
    "    # # INSERT YOUR CODE HERE\n",
    "    # # ***************************************************\n",
    "    # raise NotImplementedError\n",
    "    ### END SOLUTION\n",
    "\n",
    "\n",
    "test(compute_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.660379Z",
     "iopub.status.busy": "2025-09-11T15:37:23.660306Z",
     "iopub.status.idle": "2025-09-11T15:37:23.672094Z",
     "shell.execute_reply": "2025-09-11T15:37:23.671873Z"
    }
   },
   "outputs": [],
   "source": [
    "ps = [\n",
    "    compute_p(X, m, s) for m, s in zip(means, sigmas)\n",
    "]  # exercise: try to do this without looping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.673204Z",
     "iopub.status.busy": "2025-09-11T15:37:23.673135Z",
     "iopub.status.idle": "2025-09-11T15:37:23.684741Z",
     "shell.execute_reply": "2025-09-11T15:37:23.684551Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 0\n",
      " 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1\n",
      " 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "assignments = np.argmax(ps, axis=0)\n",
    "print(assignments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.685741Z",
     "iopub.status.busy": "2025-09-11T15:37:23.685662Z",
     "iopub.status.idle": "2025-09-11T15:37:23.752693Z",
     "shell.execute_reply": "2025-09-11T15:37:23.752398Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = np.array([\"red\", \"green\"])[assignments]\n",
    "plt.scatter(X[:, 0], X[:, 1], c=colors, s=100)\n",
    "plt.scatter(np.array(means)[:, 0], np.array(means)[:, 1], marker=\"*\", s=200)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VsIOpA8QmhYI"
   },
   "source": [
    "Solution\n",
    "==="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.754022Z",
     "iopub.status.busy": "2025-09-11T15:37:23.753905Z",
     "iopub.status.idle": "2025-09-11T15:37:23.767073Z",
     "shell.execute_reply": "2025-09-11T15:37:23.766797Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Your `compute_log_p` passed 1 tests.\n"
     ]
    }
   ],
   "source": [
    "def compute_log_p(X, mean, sigma):\n",
    "    \"\"\"\n",
    "    Compute the log probability of each data point in X under a Gaussian distribution\n",
    "\n",
    "    Args:\n",
    "        X: (n, d) numpy array, where each row corresponds to a data point\n",
    "        mean: (d, ) numpy array, the mean of the Gaussian distribution\n",
    "        sigma: (d, d) numpy array, the covariance matrix of the Gaussian distribution\n",
    "\n",
    "    Returns:\n",
    "        log_p: (n, ) numpy array, the log probability of each data point\n",
    "\n",
    "    >>> compute_log_p(np.array([[0, 0], [1, 1]]), np.array([0, 0]), np.eye(2))\n",
    "    array([-1.83787707, -2.83787707])\n",
    "    \"\"\"\n",
    "    ### SOLUTION\n",
    "    d = X.shape[1]\n",
    "    dxm = X - mean\n",
    "    exponent = -0.5 * np.sum(dxm * np.dot(dxm, np.linalg.inv(sigma)), axis=1)\n",
    "    return exponent - np.log(2 * np.pi) * (d / 2) - 0.5 * np.log(np.linalg.det(sigma))\n",
    "\n",
    "    ### TEMPLATE\n",
    "    # # ***************************************************\n",
    "    # # INSERT YOUR CODE HERE\n",
    "    # # ***************************************************\n",
    "    # raise NotImplementedError\n",
    "    ### END SOLUTION\n",
    "\n",
    "\n",
    "test(compute_log_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.768101Z",
     "iopub.status.busy": "2025-09-11T15:37:23.768029Z",
     "iopub.status.idle": "2025-09-11T15:37:23.780535Z",
     "shell.execute_reply": "2025-09-11T15:37:23.780302Z"
    }
   },
   "outputs": [],
   "source": [
    "log_ps = [\n",
    "    compute_log_p(X, m, s) for m, s in zip(means, sigmas)\n",
    "]  # exercise: try to do this without looping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.781702Z",
     "iopub.status.busy": "2025-09-11T15:37:23.781593Z",
     "iopub.status.idle": "2025-09-11T15:37:23.793495Z",
     "shell.execute_reply": "2025-09-11T15:37:23.793278Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 0\n",
      " 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1\n",
      " 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "assignments = np.argmax(log_ps, axis=0)\n",
    "print(assignments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-09-11T15:37:23.794521Z",
     "iopub.status.busy": "2025-09-11T15:37:23.794455Z",
     "iopub.status.idle": "2025-09-11T15:37:23.850300Z",
     "shell.execute_reply": "2025-09-11T15:37:23.850018Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = np.array([\"red\", \"green\"])[assignments]\n",
    "plt.scatter(X[:, 0], X[:, 1], c=colors, s=100)\n",
    "plt.scatter(np.array(means)[:, 0], np.array(means)[:, 1], marker=\"*\", s=200)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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