HW4_Problem3_solution.ipynb

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        "<a href=\"https://colab.research.google.com/github/shuwenericlei/be183/blob/main/HW4_Problem3_solution.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MozW3XxY8ezr"
      },
      "source": [
        "Bi/Be/Cs 183 2022-2023: Intro to Computational Biology\n",
        "TAs: Meichen Fang, Tara Chari, Zitong (Jerry) Wang\n",
        "\n",
        "**Submit your notebooks by sharing a clickable link with Viewer access. Link must be accessible from submitted assignment document.**\n",
        "\n",
        "Make sure Runtime $\\rightarrow$ Restart and run all works without error"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mu4obGyqS8fh"
      },
      "source": [
        "**HW 4 Problem 3**\n",
        "\n",
        "In this problem you will develop code for running the EM algorithm to fit a Gaussian Mixture Model (GMM). You will learn the mixture weights for a set of (multivariate) Gaussian distributions, which describe the input, single-cell data. This is a common approach to determine clusters within a dataset.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fJ8J92ntz2rk"
      },
      "source": [
        "##**Import data and install packages**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rjy8W5hly24q"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import scipy.io as sio\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt #Can use other plotting packages like seaborn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0Ep8gQNCNLHr"
      },
      "outputs": [],
      "source": [
        "import time\n",
        "t=time.time()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
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            "136e0fb8dff74d55ae368408a6065d16",
            "fb4227f5a8d14dd5ba4d8fca34e51c96",
            "6a767101a53e42b3b7732398ecce26c5",
            "0e030039f10a43518217b2f74e3fe363",
            "ea79eb2922f54f59ac0c4e3d32e389de",
            "7875473405764df4bf10e8338d7f301b",
            "bfe7c44243ae4140bccabae056b93ef4"
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      "outputs": [
        {
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          "name": "stderr",
          "text": [
            "<ipython-input-3-6c7d4cfd6c14>:24: TqdmDeprecationWarning: Please use `tqdm.notebook.trange` instead of `tqdm.tnrange`\n",
            "  pbar = tnrange(int(total_length/1024), unit=\"B\")\n"
          ]
        },
        {
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              "  0%|          | 0/94578 [00:00<?, ?B/s]"
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          "metadata": {}
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        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'D1.2315.gz'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "#Download count matrix of cell by gene counts and metadata files, DOI: 10.22002/D1.2315\n",
        "#tar.gz file which has:\n",
        "#(1) count matrix \n",
        "#(2) metadata for cells (cell type, date of experimental run) \n",
        "#(3) metadata for genes (gene names)\n",
        "\n",
        "import requests\n",
        "from tqdm import tnrange, tqdm_notebook\n",
        "def download_file(doi,ext):\n",
        "    url = 'https://api.datacite.org/dois/'+doi+'/media'\n",
        "    r = requests.get(url).json()\n",
        "    netcdf_url = r['data'][0]['attributes']['url']\n",
        "    r = requests.get(netcdf_url,stream=True)\n",
        "    #Set file name\n",
        "    fname = doi.split('/')[-1]+ext\n",
        "    #Download file with progress bar\n",
        "    if r.status_code == 403:\n",
        "        print(\"File Unavailable\")\n",
        "    if 'content-length' not in r.headers:\n",
        "        print(\"Did not get file\")\n",
        "    else:\n",
        "        with open(fname, 'wb') as f:\n",
        "            total_length = int(r.headers.get('content-length'))\n",
        "            pbar = tnrange(int(total_length/1024), unit=\"B\")\n",
        "            for chunk in r.iter_content(chunk_size=1024):\n",
        "                if chunk:\n",
        "                    pbar.update()\n",
        "                    f.write(chunk)\n",
        "        return fname\n",
        "\n",
        "download_file('10.22002/D1.2315','.gz')\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "31SK6rfgnkyw",
        "outputId": "88393f4a-32b8-44b8-8319-73454bc0628b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "biccnGeneMeta.csv\n",
            "biccnMeta.csv\n",
            "biccn.mtx\n"
          ]
        }
      ],
      "source": [
        "!mv D1.2315.gz biccn.tar.gz\n",
        "!tar -xvf biccn.tar.gz"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PpeuucqgiDPx"
      },
      "source": [
        "## **Read in data for analysis**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "swY2nSDukmXg"
      },
      "source": [
        "**The dataset**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NKSN3bu8cQ3O"
      },
      "source": [
        "This dataset maps the cells in the mouse primary cortex (MOp), including neuronal and non-neuronal cell types, for a total of 10 cell types ([Yao et al., 2021](https://www.nature.com/articles/s41586-021-03500-8)). We will be dealing with the 10x sequenced data only.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "58nQkH9eko4-"
      },
      "source": [
        "**The count matrix**\n",
        "\n",
        "This matrix is 18,744 cells by 5,000 genes. The full dataset contains 71,365 cells, however we will work with a randomly subsetted version to facilitate calculations within the Colab environment.\n",
        "\n",
        "1.   For each cell, gene counts were normalized to have the same number of total counts (usually 1e5 or 1e6), with cell-gene counts thus scaled accordingly.\n",
        "\n",
        "2.   Counts were then log-normalized, using the log(1+x), where x is each cell's gene count. The 1 accounts for 0 count genes. \n",
        "\n",
        "3. The ~5000 genes were selected for those that displayed large variance in expression amongst the cells ('highly variable genes').\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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          "height": 35
        },
        "id": "tZ1h_dME8vJb",
        "outputId": "5d02a02f-36af-42b8-c267-9ccb18e89c10"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(18744, 5000)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "#Get gene count matrix\n",
        "count_mat = sio.mmread('biccn.mtx')\n",
        "\n",
        "count_mat = count_mat.todense() #Make dense since most functions we'll use don't work with sparse matrices\n",
        "count_mat.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
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          "height": 238
        },
        "id": "NFissu8VB92P",
        "outputId": "156e18af-5de3-4ae7-b63f-a7f9378c502f"
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      "outputs": [
        {
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              "                                         cell_type\n",
              "barcode                                           \n",
              "AAACGAAGTGGATTTC-3L8TX_181211_01_A01       L2/3 IT\n",
              "AAACGCTCAATGCTCA-3L8TX_181211_01_A01       L2/3 IT\n",
              "AAAGTCCGTGTATCCA-3L8TX_181211_01_A01  L6 CT Cpa6_1\n",
              "AAAGTGAGTCGCCACA-3L8TX_181211_01_A01       L2/3 IT\n",
              "AAAGTGATCGTCTACC-3L8TX_181211_01_A01       L2/3 IT"
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              "                                                     [key], {});\n",
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              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "  "
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          },
          "metadata": {},
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        }
      ],
      "source": [
        "#Get metadata dataframe for the 18,744 cells (rows of the matrix)\n",
        "meta = pd.read_csv('biccnMeta.csv',index_col = 0)\n",
        "meta.head()"
      ]
    },
    {
      "cell_type": "code",
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        "id": "M5je0CyVN4DN",
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      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                                         gene_name\n",
              "Rp1_ENSMUSG00000025900      Rp1_ENSMUSG00000025900\n",
              "Sox17_ENSMUSG00000025902  Sox17_ENSMUSG00000025902\n",
              "Oprk1_ENSMUSG00000025905  Oprk1_ENSMUSG00000025905\n",
              "St18_ENSMUSG00000033740    St18_ENSMUSG00000033740\n",
              "Sntg1_ENSMUSG00000025909  Sntg1_ENSMUSG00000025909"
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              "      <td>Sox17_ENSMUSG00000025902</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Oprk1_ENSMUSG00000025905</th>\n",
              "      <td>Oprk1_ENSMUSG00000025905</td>\n",
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              "      <th>St18_ENSMUSG00000033740</th>\n",
              "      <td>St18_ENSMUSG00000033740</td>\n",
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              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-55ed847b-1402-4265-9e84-8c60e4e792f0 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-55ed847b-1402-4265-9e84-8c60e4e792f0');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "#Get metadata dataframe for the 5,000 genes (columns of the matrix)\n",
        "\n",
        "meta_gene = pd.read_csv('biccnGeneMeta.csv',index_col = 0)\n",
        "meta_gene.head()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u2DFUfz9OGGd"
      },
      "source": [
        "## **Problem 3 (30 points)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jtx3LM4-Skv8"
      },
      "source": [
        "Gaussian mixture model (GMM) is as defined below:\n",
        "\n",
        "\\begin{align}\n",
        "f_{GMM}(\\mathbf{x})=\\sum_{j=1}^k \\phi_j f(\\mathbf {x};{\\boldsymbol{\\mu }}_{j},\\mathbf{\\Sigma}_{j})\n",
        "\\end{align}\n",
        "subject to $\\sum_{j=1}^k \\phi_j = 1$.\n",
        "\n",
        "$\\boldsymbol{\\phi}$ denotes the weights for each Gaussian pdf $f$, and together the GMM is defined as the weighted sum of these Gaussians. $\\boldsymbol{\\mu} \\text{ and } \\mathbf{\\Sigma}$ represent the mean (vector) and covariance (matrix) for each of the $k$ multivariate Gaussians. This model can then describe data with multiple modes/areas of high density i.e. $k$ cell types which shared distinct gene expression signatures."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cuXYuplhT87h"
      },
      "source": [
        "Let $\\mathbf{x} = (\\mathbf{x}_1, \\mathbf{x}_2, \\ldots \\mathbf{x}_n)$ be $n$ independent observations (e.g. cells) which come from a mixture of Gaussians. They are $d$ dimensional, where $d$ is the number of gene measurements. We will define $\\mathbf{z} = (z_1, z_2, \\ldots z_n)$ as the latent variable which represents the mixture component (of the $k$ components) which a cell comes from. Thus $\\phi_j = P(Z = j)$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O130zlbuVrjz"
      },
      "source": [
        "The parameters to be fit, $\\theta = (\\boldsymbol{\\mu}_1,\\ldots \\boldsymbol{\\mu}_k, \\mathbf{\\Sigma_1}, \\ldots \\mathbf{\\Sigma_k}, \\mathbf{\\phi}_1, \\ldots \\mathbf{\\phi}_k)$ (the parameters of the GMM)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1TE_28ohWNUh"
      },
      "source": [
        "The (complete) likelihood for maximization is defined as \n",
        "\\begin{align}\n",
        "p(\\mathbf {x},\\mathbf {z};\\theta) =\\prod _{i=1}^{n}\\prod _{j=1}^{k}\\ [f(\\mathbf {x} _{i};{\\boldsymbol{\\mu }}_{j},\\mathbf{\\Sigma}_{j})\\phi_{j}]^{\\mathbb {I} (z_{i}=j)}\n",
        "\\end{align}\n",
        "\n",
        "where $\\mathbb {I}$ is the indicator function.\n",
        "\n",
        "As described in Problem 1, we will use the $Q$ function to maximize, where \n",
        "\\begin{align}\n",
        "Q(\\theta|\\theta_t) = E_{\\mathbf {z}|\\mathbf {x},\\theta_t} [\\log(p(\\mathbf {x},\\mathbf {z};\\theta))].\n",
        "\\end{align}\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CcNeuEG8lIEN"
      },
      "source": [
        "Dimensions of variables ($n$ cells, $d$ genes):\n",
        "\n",
        "$\\mathbf{X}: n\\times d$ matrix\n",
        "\n",
        "$\\boldsymbol{\\mu}: k \\times d$ matrix\n",
        "\n",
        "$\\boldsymbol{\\Sigma}: k\\times d \\times d$ matrix\n",
        "\n",
        "$\\boldsymbol{\\phi}:$ 1d array of length $k$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9X5uTrNgSrVU"
      },
      "source": [
        "### **a) Often covariance matrices of single-cell datasets are singular (non-invertible). Subset the input matrix X to create a 'regularized'-non-singular matrix to use.(5 points)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S14pcM1aTAyt"
      },
      "source": [
        "Remove the bottom half of genes based on variance i.e. calculate the variance of expression for *each* gene and remove any genes below the mean variance (from across all genes). In this sense we are further removing 'redundancy' from the matrix.\n",
        "\n",
        "Remember that the counts of the matrix are log1p() of the original counts.\n",
        "\n",
        "**Report how many genes remain after this subsetting, and use this subsetted matrix for all downstream calculations.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "h63VPYXeTARQ"
      },
      "outputs": [],
      "source": [
        "ori_counts=np.exp(count_mat)-1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kz-4kjJ_TATb",
        "outputId": "34fdbffa-97f1-4c03-d770-fdd787f99390"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(18744, 97)"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "gene_var=np.ravel(np.var(ori_counts, axis=0))\n",
        "mean = np.mean(gene_var)\n",
        "idx = gene_var > mean\n",
        "\n",
        "counts=count_mat[:,idx]\n",
        "counts.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dsjZF3LAziHA"
      },
      "outputs": [],
      "source": [
        "X=counts"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y8oMK4OkOVGZ"
      },
      "source": [
        "### **b) Implement the E step (5 points)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Plo-CevdOXeb"
      },
      "source": [
        "For the E step we assume a set of (randomly initialized) $\\theta_t$.\n",
        "Then:\n",
        "\\begin{align}\n",
        "Q(\\theta|\\theta_t) &= \\sum_{i=1}^{n} \\sum_{j=1}^{k} P(Z_i = j | X_i = \\mathbf{x}_i; \\theta_t) \\log(p(\\mathbf {x}_i,j;\\theta_j)) \\\\\n",
        " &= \\sum_{i=1}^{n} \\sum_{j=1}^{k} T_{i,j}^t[\\log \\phi _{j}-{\\tfrac {1}{2}}\\log |\\mathbf{\\Sigma} _{j}|-{\\tfrac {1}{2}}(\\mathbf {x} _{i}-{\\boldsymbol {\\mu }}_{j})^{\\top }\\mathbf{\\Sigma} _{j}^{-1}(\\mathbf {x} _{i}-{\\boldsymbol {\\mu }}_{j})-{\\tfrac {d}{2}}\\log(2\\pi )]\n",
        "\\end{align}\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SeA2jtM-n_v9"
      },
      "source": [
        "$T_{i,j}^t$ represents $P(Z_i = j | X_i = \\mathbf{x}_i; \\theta_t)$ and $p(\\mathbf {x}_i,j;\\theta_j) = f(\\mathbf {x} _{i};{\\boldsymbol{\\mu }}_{j},\\mathbf{\\Sigma}_{j})\\phi_{j}$.\n",
        "\n",
        "$T_{i,j}^t$ needs to be calculated given the current $\\theta_t$ for every $\\mathbf{x}_i$ in the E step.\n",
        "\n",
        "Using Bayes theorem we can get that \n",
        "\\begin{align}\n",
        "T_{i,j}^t = \\frac {\\phi _{j}^{t}\\ f(\\mathbf {x} _{i};{\\boldsymbol {\\mu }}_{j}^{t},\\mathbf{\\Sigma} _{j}^{t})}{\\sum_{r=1}^k \\phi _{r}^{t}\\ f(\\mathbf {x} _{i};{\\boldsymbol {\\mu }}_{r}^{t},\\mathbf{\\Sigma} _{r}^{t})}\n",
        "\\end{align}\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "soHVlU_sRKAe"
      },
      "source": [
        "You can use [scipy.stats multivariate_normal.pdf](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.multivariate_normal.html) to calculate $f$ and [numpy cov](https://numpy.org/doc/stable/reference/generated/numpy.cov.html) to calculate covariances."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FBdvGVNqsv-e"
      },
      "source": [
        "**Fill in the e_step() function and calculate the matrix $\\mathbf{T}$ given inputs $\\mathbf{X}, \\boldsymbol{\\mu^t}, \\mathbf{\\Sigma^t}, \\textbf{ and } \\boldsymbol{\\phi^t}$. $\\mathbf{X}$  represents our cell x genes data matrix.**\n",
        "\n",
        "Note: You may need to add a small epsilon ($\\approx$ 1e-100) to $f$ values, to avoid divide by zero errors."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "INVAvW2EC_dc"
      },
      "outputs": [],
      "source": [
        "from scipy.stats import multivariate_normal"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HfisvYTyODwK"
      },
      "outputs": [],
      "source": [
        "def e_step(X, Mu, Sigma, phi):\n",
        "  '''\n",
        "  Parameters:\n",
        "   X: n*d matrix\n",
        "   Mu: k*d matrix\n",
        "   Sigma: k*d*d tensor\n",
        "   phi: 1d array of length k\n",
        "  '''\n",
        "  eps = 10e-100\n",
        "  n,d=X.shape \n",
        "  k=len(Mu) \n",
        "  f = np.zeros((n,k))\n",
        "  for j in range(k):\n",
        "    f[:,j] = multivariate_normal.pdf(X, mean=Mu[j], cov=Sigma[j], allow_singular=True)\n",
        "  f=f+eps\n",
        "  p=phi[None,:]*f\n",
        "  T= p/np.sum(p,axis=1)[:,None]\n",
        "  return T, f"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4kqrqo5GOkEp"
      },
      "source": [
        "### **c) Implement the M step (5 points)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JPme3tp7qRo4"
      },
      "source": [
        "In the maximization (M) step, we then (re-)calculate the MLE values for $\\theta$ or $(\\boldsymbol{\\mu}_1,\\ldots \\boldsymbol{\\mu}_k, \\mathbf{\\Sigma}_1, \\ldots \\mathbf{\\Sigma}_k, \\mathbf{\\phi}_1, \\ldots \\mathbf{\\phi}_k)$ at this $t+1$ step. \n",
        "\n",
        "Here $j$ is from 1 to k."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bvVv0qwjqqqy"
      },
      "source": [
        "For $\\boldsymbol{\\phi}$\n",
        "\\begin{align}\n",
        "\\phi _{j} ={\\frac {1}{n}}\\sum _{i=1}^{n}T_{i,j}^{t}.\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "For $\\boldsymbol{\\mu}$\n",
        "\\begin{align}\n",
        "\\boldsymbol{\\mu}_j = \\frac{\\sum_{i=1}^n T_{i,j}^{t} \\mathbf{x}_i}{\\sum_{i=1}^n T_{i,j}^{t}}.\n",
        "\\end{align}\n",
        "\n",
        "And for $\\boldsymbol{\\Sigma}$\n",
        "\\begin{align}\n",
        "\\mathbf{\\Sigma}_j = \\frac{\\sum_{i=1}^n T_{i,j}^{t} (\\mathbf{x}_i - \\boldsymbol{\\mu}_j)^\\top (\\mathbf{x}_i - \\boldsymbol{\\mu}_j) }{\\sum_{i=1}^n T_{i,j}^{t}}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "typSX-yJsyWw"
      },
      "source": [
        "**Fill in the m_step() function to calculate the updated $\\boldsymbol{\\mu}, \\mathbf{\\Sigma}, \\textbf{ and } \\boldsymbol{\\phi}$ values given $\\mathbf{T}$.**\n",
        "\n",
        "Note: To calculate the new covariance matrices you can use the aweights input option for [np.cov](https://numpy.org/doc/stable/reference/generated/numpy.cov.html), where the $T^t_{i,j}$ values are the weights."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CyFM88e7Ok7J"
      },
      "outputs": [],
      "source": [
        "def m_step(X, T):\n",
        "  n,d=np.shape(X) \n",
        "  n,k=np.shape(T)\n",
        "  phi = np.mean(T,axis=0)\n",
        "  Mu = np.zeros((k,d))\n",
        "  Sigma = np.zeros((k,d,d))\n",
        "  for j in range(k):\n",
        "    t = T[:, [j]]\n",
        "    total_t = t.sum()\n",
        "    Mu[j,:] = (t.T@X).sum(axis=0) / total_t\n",
        "    Sigma[j] = np.cov(X.T, aweights=(t/total_t).flatten(), bias=True)\n",
        "  return Mu, Sigma, phi"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HYJQW5CROmPC"
      },
      "source": [
        "### **d) Run EM steps for 100 iterations and get mixture (cluster) assignments for the cells. (10 points)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mjxCPu_6s28W"
      },
      "source": [
        "To initialize the EM process we will (1) let $k = 10$ (also the number of labeled cell types), (2) assume $\\boldsymbol{\\phi}$ has a uniform probability for each $k$, (3) choose random rows from the data to represent each of the $k$  $\\boldsymbol{\\mu}$s, and (4) use the covariance matrix for $\\mathbf{X}$ (the cell x genes matrix) to intialize the $k$ $\\mathbf{\\Sigma}$s.\n",
        "\n",
        "Run the EM algorithm for 100 iterations.\n",
        "\n",
        "** **"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1nT6tKWTvL_P"
      },
      "source": [
        "Determine the final cluster assignment for each cell $i$ by finding which $k$ (mixture component) has the max $T_{i,j}$ value."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RV2NAmy3s6yM"
      },
      "source": [
        "**Plot Q over the iterations, and report $\\boldsymbol{\\phi}$ and the cluster (k) assignments for the first 10 cells after 100 iterations.**\n",
        "\n",
        "**You can use the initialization provided below.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pGrKFfdIIsPM"
      },
      "outputs": [],
      "source": [
        "def EM(X, Mu, Sigma, phi, iterations=100):\n",
        "  Q=np.zeros(iterations)\n",
        "  old_T, f = e_step(X, Mu, Sigma, phi)\n",
        "  Mu, Sigma, phi = m_step(X, old_T)\n",
        "  for i in range(iterations):\n",
        "    new_T, f = e_step(X, Mu, Sigma, phi)\n",
        "    q = np.sum(old_T*np.log(phi*f))\n",
        "    Mu, Sigma, phi = m_step(X, new_T)\n",
        "    old_T = new_T\n",
        "    Q[i] = q\n",
        "  return new_T, Mu, Sigma, phi, Q"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8n5Nd3dMs2N2"
      },
      "outputs": [],
      "source": [
        "n,d=X.shape\n",
        "k=10\n",
        "np.random.seed(2022)\n",
        "init_idx=np.random.choice(n,k,replace=False)\n",
        "Mu0=np.asarray(X[init_idx,:])\n",
        "Sigma0=[ np.cov(X.T) for _ in range(k) ]\n",
        "phi0=np.ones(k)/k"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "q4aGFfYiBIqb"
      },
      "outputs": [],
      "source": [
        "T, Mu, Sigma, phi, Q = EM(X, Mu0, Sigma0,  phi0, iterations=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "l3zF7UD7NAgu"
      },
      "outputs": [],
      "source": [
        "cluster_assig=np.argmax(T, axis=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vudRdaQDZ92o",
        "outputId": "92b49a35-bf81-4111-9c14-133f26fcaca3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "𝜙 is  [0.01916477 0.04064866 0.00914755 0.036432   0.03432795 0.07456357\n",
            " 0.27759634 0.35443737 0.01313044 0.14055134]\n"
          ]
        }
      ],
      "source": [
        "print(\"𝜙 is \", phi)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Be0WnrsmaHWs",
        "outputId": "2ef5e938-4865-4507-b852-fa086ad7ff99"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The cluster (k) assignments for first 10 cells are  [7 7 6 7 7 7 3 5 9 9]\n"
          ]
        }
      ],
      "source": [
        "print(\"The cluster (k) assignments for first 10 cells are \", cluster_assig[:10])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "DZhsv_umt0e4",
        "outputId": "c953db2d-cf15-4a1d-c1b3-26db7445e164"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.plot(Q,'.')\n",
        "plt.title(\"Q in each iterations\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s6YAyezbPTgp"
      },
      "source": [
        "### **e) Calculate correspondence of generated clusters and given cell type labels. (5 points)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IIr-6MaXUyLQ"
      },
      "source": [
        "For each mixture component/cluster of cells, find the majority cell type label and the percent of cells with that label.\n",
        "\n",
        "**Report the percent of cells with the majority label for each cluster and what that majority label is.**\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "35m709X_QRre",
        "outputId": "59e582c8-6294-406f-fa95-e0b94e0dee54"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "In the 0th cluster, 0.52 of cells have the majority label of Vip Chat\n",
            "In the 1th cluster, 0.71 of cells have the majority label of L6 CT Cpa6_1\n",
            "In the 2th cluster, 0.54 of cells have the majority label of Vip Chat\n",
            "In the 3th cluster, 0.87 of cells have the majority label of L5 NP Slc17a8_1\n",
            "In the 4th cluster, 0.51 of cells have the majority label of Vip Chat\n",
            "In the 5th cluster, 1.0 of cells have the majority label of L2/3 IT\n",
            "In the 6th cluster, 1.0 of cells have the majority label of L6 CT Cpa6_1\n",
            "In the 7th cluster, 0.98 of cells have the majority label of L2/3 IT\n",
            "In the 8th cluster, 0.69 of cells have the majority label of Vip Chat\n",
            "In the 9th cluster, 1.0 of cells have the majority label of L2/3 IT\n"
          ]
        }
      ],
      "source": [
        "lables=cluster_assig\n",
        "for j in range(k):\n",
        "    # find cell idx\n",
        "    cell_idx = np.where(lables==j)[0]\n",
        "    if len(cell_idx)==0:\n",
        "      continue\n",
        "    # count cell type label\n",
        "    cell_type = meta.iloc[cell_idx][\"cell_type\"].tolist()\n",
        "    # find the majority cell type label and percent\n",
        "    percents=[cell_type.count(x)/len(cell_type) for x in np.unique(cell_type)]\n",
        "    label_idx = np.argmax(percents)\n",
        "    print(\"In the \"+ str(j) +\"th cluster, \" + str(np.around(percents[label_idx],2)) + \" of cells have the majority label of \" + cell_type[label_idx])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "77ulExyGpjwI",
        "outputId": "86aff313-d13f-450b-a1fb-fde9851ca8ca"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3.81110733350118 mins\n"
          ]
        }
      ],
      "source": [
        "t=time.time()-t\n",
        "print(t/60,'mins')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H1eP8x6SgpSB"
      },
      "source": [
        "### **Now let's compare to sklearn package (Not in homework)**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "id": "ArJgkd6S3ose",
        "outputId": "17b5fa26-5024-42d5-a29e-1e6ba9776f6c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/sklearn/utils/validation.py:593: FutureWarning: np.matrix usage is deprecated in 1.0 and will raise a TypeError in 1.2. Please convert to a numpy array with np.asarray. For more information see: https://numpy.org/doc/stable/reference/generated/numpy.matrix.html\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "from sklearn.decomposition import PCA\n",
        "pca = PCA(svd_solver='full') # if n_components is not set all components are kept\n",
        "pca.fit(X)\n",
        "\n",
        "labels=cluster_assig\n",
        "y_pca = np.array(X@pca.components_.T[:,:2])\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "for i,cell_type in enumerate(np.unique(labels)):\n",
        "  idx = np.where( labels == cell_type)\n",
        "  ax.scatter(y_pca[idx,0], y_pca[idx,1], color = list(plt.cm.tab10(i)), label = cell_type)\n",
        "ax.legend(loc=(1.1,0.2), title=\"Cell types\")\n",
        "ax.set_xlabel(\"PC1\")\n",
        "ax.set_ylabel(\"PC2\")\n",
        "ax.set_title(\"GMM labels\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xkjCpzo9qU2i"
      },
      "outputs": [],
      "source": [
        "from sklearn.mixture import GaussianMixture"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hnrgYZWS8Kda",
        "outputId": "6098c881-52df-411b-b15d-f8867d9e2fce"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/sklearn/utils/validation.py:593: FutureWarning: np.matrix usage is deprecated in 1.0 and will raise a TypeError in 1.2. Please convert to a numpy array with np.asarray. For more information see: https://numpy.org/doc/stable/reference/generated/numpy.matrix.html\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.8/dist-packages/sklearn/utils/validation.py:593: FutureWarning: np.matrix usage is deprecated in 1.0 and will raise a TypeError in 1.2. Please convert to a numpy array with np.asarray. For more information see: https://numpy.org/doc/stable/reference/generated/numpy.matrix.html\n",
            "  warnings.warn(\n"
          ]
        }
      ],
      "source": [
        "gm=GaussianMixture(n_components=k,means_init=Mu0,weights_init=phi0,max_iter=100).fit(X)\n",
        "gm_clusters=gm.predict(X)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PYx5L34IZxiy",
        "outputId": "edf4ffb6-6e36-4df0-f115-3c483715aae2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "In the 0th cluster, 1.0 of cells have the majority label of L2/3 IT\n",
            "In the 1th cluster, 1.0 of cells have the majority label of L6 CT Cpa6_1\n",
            "In the 2th cluster, 0.61 of cells have the majority label of Vip Chat\n",
            "In the 3th cluster, 1.0 of cells have the majority label of L2/3 IT\n",
            "In the 4th cluster, 1.0 of cells have the majority label of Endo Slc38a5_1\n",
            "In the 5th cluster, 0.47 of cells have the majority label of L5 ET_1\n",
            "In the 6th cluster, 1.0 of cells have the majority label of Astro Aqp4\n",
            "In the 7th cluster, 0.58 of cells have the majority label of L5 NP Slc17a8_1\n",
            "In the 8th cluster, 1.0 of cells have the majority label of L6 CT Cpa6_1\n",
            "In the 9th cluster, 1.0 of cells have the majority label of L2/3 IT\n"
          ]
        }
      ],
      "source": [
        "lables=gm_clusters\n",
        "for j in range(k):\n",
        "    # find cell idx\n",
        "    cell_idx = np.where(lables==j)[0]\n",
        "    # count cell type label\n",
        "    cell_type = meta.iloc[cell_idx][\"cell_type\"].tolist()\n",
        "    # find the majority cell type label and percent\n",
        "    percents=[cell_type.count(x)/len(cell_type) for x in np.unique(cell_type)]\n",
        "    label_idx = np.argmax(percents)\n",
        "    print(\"In the \"+ str(j) +\"th cluster, \" + str(np.around(percents[label_idx],2)) + \" of cells have the majority label of \" + cell_type[label_idx])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "v8jTfAo1yyHT",
        "outputId": "19af1525-3498-42b7-ec3d-ab85e3033576"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "labels=gm_clusters\n",
        "y_pca = np.array(X@pca.components_.T[:,:2])\n",
        "\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "for i,cell_type in enumerate(np.unique(labels)):\n",
        "  idx = np.where( labels == cell_type)\n",
        "  ax.scatter(y_pca[idx,0], y_pca[idx,1], color = list(plt.cm.tab10(i)), label = cell_type, alpha=0.5)\n",
        "ax.legend(loc=(1.1,0.2), title=\"Cell types\")\n",
        "ax.set_xlabel(\"PC1\")\n",
        "ax.set_ylabel(\"PC2\")\n",
        "ax.set_title(\"sklearn GMM lables\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "XmYuQJfW0_w1",
        "outputId": "996320cf-a39a-489b-e641-0e209adca464"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "labels=meta[\"cell_type\"]\n",
        "y_pca = np.array(X@pca.components_.T[:,:2])\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "for i,cell_type in enumerate(np.unique(labels)):\n",
        "  idx = np.where( labels == cell_type)\n",
        "  ax.scatter(y_pca[idx,0], y_pca[idx,1], color = list(plt.cm.tab10(i)), label = cell_type, alpha=0.5)\n",
        "ax.legend(loc=(1.1,0.2), title=\"Cell types\")\n",
        "ax.set_xlabel(\"PC1\")\n",
        "ax.set_ylabel(\"PC2\")\n",
        "ax.set_title(\"cell type labels\")\n",
        "plt.show()"
      ]
    },
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