3_BayesianMixture.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gpWVp3N7zVv3"
      },
      "source": [
        "# 2-D Bayesian mixture of distributions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nWIorb2gzVv4"
      },
      "source": [
        "This code example explores a Bayesian mixture of normal distributions in two dimensions and generates samples from it. Bayesian means that the parameters of the mixture, that is the mixing coefficients, and the mean and covariance matrix of each component follow themselves a distribution. The number of components, $K$ remains fixed.\n",
        "\n",
        "<font color='red'> The mixing coefficients are sampled from a distribution. If that distribution is flat or uninformative, all cluster sizes are possible. That distribution can be peaked to make certain cluster sizes more likely, but there is always a non-zero possibility for any cluster size. </font>\n",
        "\n",
        "In particular, $\\boldsymbol{\\pi} =(\\pi_1, \\ldots, \\pi_K)$ follows a Dirichlet distribution with parameter $\\boldsymbol{\\alpha} = (\\alpha/K, \\ldots, \\alpha/K)^T$. $\\alpha$ is a hyperparamter. If it is equal to $K$, then the Dirichlet distribution is the uniform distribution and all vectors of mixing coefficients are equally likely.\n",
        "\n",
        "<font color='red'> The distribution from which the normal distributions are drawn has four hyperparameters (hyper, since they are parameters to determine other paramters). </font>\n",
        "- <font color='red'> The location vector is where the means of the sampled distributions are grouped. </font>\n",
        "- <font color='red'> The inverse scale matrix is where the covariance matrices are grouped. </font>\n",
        "- <font color='red'> The degrees of freedom control how similar the sampled distributions need to look to the location vector and inverse scale matrix. </font>\n",
        "- <font color='red'> The mean fraction controls how overlapping the clusters are. </font>\n",
        "\n",
        "Each normal distribution with mean $\\boldsymbol{\\mu}_k$ and covariance matrix $\\boldsymbol{\\Sigma}_k$, can be drawn from the *normal inverse Wishart distribution*, $(\\boldsymbol{\\mu}_k, \\boldsymbol{\\Sigma}_k) \\sim \\textrm{NIW}(\\mathbf{m}, \\lambda, \\boldsymbol{\\Psi}, \\nu)$, with four hyperparameters:\n",
        "- the *location vector* $\\mathbf{m}$ lying in the feature space,\n",
        "- the *inverse scale matrix* $\\boldsymbol{\\Psi}$, which has to be symmetric and positive definite,\n",
        "- $\\nu$, which has to be at least the number of dimensions $d$ of the feature space and regulates the degrees of freedom,\n",
        "- the *mean fraction* $\\lambda$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pN1iJuOSzVv5"
      },
      "source": [
        "## Import modules"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "8w7khG52zVv6"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import scipy.stats as ss\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NXGww_OHzVv7"
      },
      "source": [
        "## Generate samples\n",
        "This is implemented as a function."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "rs_5sRWKzVv7"
      },
      "outputs": [],
      "source": [
        "def BayesianMixture(size,n_components,alpha0,mean0,lambda0,scale,df):\n",
        "    \"\"\" Input:\n",
        "    size:           number of data points to be generated,\n",
        "    n_components:   number of clusters\n",
        "    alpha0:         concentration parameter,\n",
        "    mean0:          location vector,\n",
        "    lambda0:        mean fraction,\n",
        "    scale:          scale matrix,\n",
        "    df:             degrees of freedom.\n",
        "    Output:\n",
        "    data:           data vector,\n",
        "    idx:            index vector which process generated the sample,\n",
        "    p:              vector of mixing coefficients\n",
        "    means:          array of the means of all processes,\n",
        "    covs:           array of the covariance matrices of all processes.\"\"\"\n",
        "\n",
        "    # Generate vector of mixture coefficients from Dirichlet distribution\n",
        "    # given by alpha0 and n_components.\n",
        "    alpha = alpha0/n_components ** np.ones(n_components)\n",
        "    p= np.random.dirichlet(alpha)\n",
        "    # Generate latent indicator variable for cluster membership.\n",
        "    idx = np.random.choice(n_components, size=size, replace=True, p=p)\n",
        "    # Allocate space for the parameters of the distributions.\n",
        "    covs=np.zeros((2,2,n_components))\n",
        "    means=np.zeros((2,n_components))\n",
        "    # Generate distribution for each cluster.\n",
        "    for k in range(n_components):\n",
        "        cov=ss.invwishart.rvs(df = df, scale = scale)\n",
        "        covs[:,:,k]=cov\n",
        "        means[:,k]=np.random.multivariate_normal(mean = mean0,\n",
        "                                                 cov = 1/lambda0 * cov)\n",
        "    # Allocate space for data samples.\n",
        "    data=np.zeros((size,2))\n",
        "    # Generate data.\n",
        "    for n in range(size):\n",
        "        v=np.random.multivariate_normal(mean = means[:,idx[n]],\n",
        "                                        cov = covs[:,:,idx[n]])\n",
        "        data[n,:]=v\n",
        "    return data, idx, p, means, covs"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UfdecWmKzVv8"
      },
      "source": [
        "### Define sample size"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "4RygpEGzzVv8"
      },
      "outputs": [],
      "source": [
        "sample_size = 1000"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m2WYhbkuzVv9"
      },
      "source": [
        "### Define hyperparameters\n",
        "In this example, we use the hyperparameters,\n",
        "\\begin{equation}\n",
        "K = 3, \\alpha = K, \\mathbf{m} = \\left( 0 \\atop 0 \\right), \\lambda = 1, \\boldsymbol{\\Psi} = \\left( 1 \\atop 1.5 \\right. \\left.  1.5 \\atop 3 \\right), \\nu = 6.\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "vuTa_EyXzVv9"
      },
      "outputs": [],
      "source": [
        "K = 3\n",
        "a = K\n",
        "m = np.array([0, 0])\n",
        "lambda0 = 1;\n",
        "Psi = np.array([[1, 1.5], [1.5, 3]])\n",
        "nu = 6;"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "duaYNmfXzVv9"
      },
      "source": [
        "### Generate distributions and samples"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vZgrda1azVv-",
        "outputId": "30ae7c37-98b6-4964-a507-62e37ab3317d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mixing coefficients:  [0.15219342 0.0358626  0.81194398] \n",
            "\n",
            "Component 1\n",
            "Mean: [-1.1491841  -1.89804636]\n",
            "Covariance: [[0.8629616  1.40519997]\n",
            " [1.40519997 2.33653443]] \n",
            "\n",
            "Component 2\n",
            "Mean: [-0.15043603 -0.26982749]\n",
            "Covariance: [[0.38942612 0.43540964]\n",
            " [0.43540964 0.55547886]] \n",
            "\n",
            "Component 3\n",
            "Mean: [-0.22286754 -1.10586222]\n",
            "Covariance: [[0.28684544 0.6380798 ]\n",
            " [0.6380798  1.64744669]] \n",
            "\n"
          ]
        }
      ],
      "source": [
        "data, idx, p, means, covs = BayesianMixture(size=sample_size,n_components=K,alpha0=a,mean0=m,\n",
        "                                       lambda0=lambda0,scale=Psi,df=nu)\n",
        "print('Mixing coefficients: ', p, '\\n')\n",
        "for i in range(K):\n",
        "    print('Component', i+1)\n",
        "    print('Mean:', means[:,i])\n",
        "    print('Covariance:', covs[:,:,i], '\\n')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CKym_SkdzVv_"
      },
      "source": [
        "### Plot of probability density functions\n",
        "#### First individually"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 682
        },
        "id": "D18kWL_0zVwA",
        "outputId": "78e41c64-be47-49fd-e70c-a24eb673a483"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1400x800 with 6 Axes>"
            ],
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          },
          "metadata": {}
        }
      ],
      "source": [
        "x, y = np.mgrid[-7:4:.01, -6:5:.01]\n",
        "pos = np.dstack((x, y))\n",
        "z_all = np.zeros((x.shape[0], x.shape[1]))\n",
        "cols = 2\n",
        "rows = np.ceil(K/cols).astype(int)\n",
        "fig = plt.figure(figsize=(14,8))\n",
        "for i in range(K):\n",
        "    ax = fig.add_subplot(rows, cols, i+1)\n",
        "    z = ss.multivariate_normal.pdf(pos, mean = means[:,i], cov = covs[:,:,i])\n",
        "    z_all = z_all + z * p[i]\n",
        "    c = ax.contourf(x, y, z, cmap = plt.cm.YlGn)\n",
        "    cbar = plt.colorbar(c)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4t3ZLoyTzVwA"
      },
      "source": [
        "#### Then mixed"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        },
        "id": "-qBExe6KzVwA",
        "outputId": "298086a7-0ab6-4ff2-e281-d67fb0b5534a"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig = plt.figure()\n",
        "c = plt.contourf(x, y, z_all, cmap = plt.cm.YlGn)\n",
        "cbar = plt.colorbar(c)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7je4XsXYzVwB"
      },
      "source": [
        "### Scatter plot of samples"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "wa-BVJqazVwB",
        "outputId": "0bbe9b65-ceeb-4118-e393-5be15c016311"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1300x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig = plt.figure(figsize=(13,8))\n",
        "plt.scatter(data[:,0], data[:,1], c = idx, cmap = plt.cm.brg)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QRQ6BpKRzVwB"
      },
      "source": [
        "#### Number of samples per component"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0dONiFIDzVwB",
        "outputId": "01d9eafb-ff32-497e-eb87-046f002b9c84"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Component 1 : 157\n",
            "Component 2 : 46\n",
            "Component 3 : 797\n"
          ]
        }
      ],
      "source": [
        "for i in range(K):\n",
        "    print('Component', i+1, ':', sum(idx==i))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t3utJwB-zVwC"
      },
      "source": [
        "### Explore hyperparameters\n",
        "\n",
        "While exploring the effect of changing one hyperparameter, keep the other ones fixed.\n",
        "\n",
        "First change $\\alpha$ to $10 K$ and then $100 K$. You should notice that the vector of mixing coefficients becomes more like $(1/3, 1/3, 1/3)$ and the clusters become similar in size.\n",
        "\n",
        "Next fix $\\alpha = 10K$, and change the number of degrees of freedom, $\\nu$, to $2$ and then $10$. You should notice that in the first case very different distributions are generated, while in the second case the distirbutions are more similar to the base distribution given by $\\mathbf{m}$ and $\\boldsymbol{\\Psi}$\n",
        "\n",
        "Next fix $\\alpha = 10K$ and $\\nu = 6$, and change the mean fraction $\\lambda$ to 1/3 and then 1/5. You should notice that as $\\lambda$ decreases the clusters separate.\n",
        "\n",
        "In the next step we will infer a Bayesian mixture by adjusting the hyperparameters and sampling the parameters of the distributions."
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.6"
    },
    "colab": {
      "provenance": [],
      "toc_visible": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}