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@bamford
Created January 28, 2021 09:38
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Testing that the likelihood of a GMM doesn't depend on the number of components
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{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "%matplotlib inline",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "import numpy as np\nfrom matplotlib import pyplot as plt\nfrom sklearn.datasets import make_blobs\nfrom sklearn.mixture import GaussianMixture\nfrom sklearn.utils import check_random_state",
"execution_count": 2,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Generate some test data"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "dim = 3\nN_obs = 1000\nk_true = 3\ncluster_std = 0.22",
"execution_count": 3,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def blobs(k, d, N, seed=None):\n rnd = np.random.RandomState(seed)\n weights = rnd.uniform(0.1, 1, size=k)\n weights /= weights.sum()\n N_i = (N*weights).round().astype(np.int)\n return make_blobs(n_samples=N_i, n_features=d, cluster_std=cluster_std, center_box=(-1.0, 1.0), random_state=rnd)",
"execution_count": 4,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "X, y = blobs(k_true, dim, N_obs)",
"execution_count": 5,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.scatter(X[:, 0], X[:, 1], c=y, marker='.')\nplt.axis('equal');",
"execution_count": 6,
"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"
}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Perform a regular GMM fit"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "k=3\ngmm = GaussianMixture(n_components=k, covariance_type='diag')\ny_fit = gmm.fit_predict(X)",
"execution_count": 7,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.scatter(X[:, 0], X[:, 1], c=y_fit, marker='.')\nplt.axis('scaled');",
"execution_count": 8,
"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"
}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def stats(gmm, X):\n loglike = gmm.score(X) * len(X)\n bic = -0.5 * gmm.bic(X)\n return loglike, bic",
"execution_count": 9,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "stats(gmm, X)",
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 10,
"data": {
"text/plain": "(-726.6331612983765, -795.7107140881978)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "gmm.weights_",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
"text/plain": "array([0.23273924, 0.4806504 , 0.28661036])"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "np.sum(np.log(gmm.weights_))",
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 12,
"data": {
"text/plain": "-3.4400833027491906"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "gmm.weights_.prod()",
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 13,
"data": {
"text/plain": "0.03206201436267194"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "gmm.means_",
"execution_count": 14,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 14,
"data": {
"text/plain": "array([[-0.58956022, -0.11401122, -0.34202608],\n [ 0.50764544, -0.43519068, 0.15353586],\n [-0.67996612, -0.83889072, -0.7377096 ]])"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "np.sqrt(gmm.covariances_)",
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 15,
"data": {
"text/plain": "array([[0.21841889, 0.23282403, 0.21757054],\n [0.21526531, 0.22797553, 0.22573387],\n [0.21817523, 0.2222029 , 0.20913296]])"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Perform model selection for k"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "k_try = range(1, 10)\nmodsel = np.array([stats(GaussianMixture(n_components=k, covariance_type='diag').fit(X), X)\n for k in k_try])",
"execution_count": 16,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(k_try, modsel[:, 0], label='logL')\nplt.plot(k_try, modsel[:, 1], label='BIC')\nplt.legend()\nplt.xlabel('k');",
"execution_count": 17,
"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"
}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now create a GMM with k identical components **without fitting**"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def unit_gmm(k, dim):\n \"\"\" Create a GMM with k identical components\n \n Each component has zero mean and unit variance.\n Mixture weights are randomly assigned, such that no\n component is more than five times smaller than any other.\n \n \"\"\"\n weights_init = np.random.uniform(0.2, 1.0, size=k)\n weights_init /= weights_init.sum()\n means_init = np.zeros((k, dim))\n precisions_init = np.ones((k, dim))\n\n gmm = GaussianMixture(n_components=k, covariance_type='diag',\n weights_init=weights_init, means_init=means_init,\n precisions_init=precisions_init)\n\n random_state = check_random_state(gmm.random_state)\n gmm._initialize_parameters(np.random.normal(size=X.shape), random_state)\n gmm.covariances_ = 1/precisions_init\n return gmm",
"execution_count": 18,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "gmm = unit_gmm(3, dim)",
"execution_count": 19,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Sample from the GMM to demonstrate it is working"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "X_sample, y_sample = gmm.sample(1000)",
"execution_count": 20,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.scatter(X_sample[:, 0], X_sample[:, 1], c=y_sample, marker='.')\nplt.axis('scaled');",
"execution_count": 21,
"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"
}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Predict from the GMM: all points get same assignment (to component zero), since components are identical"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "y_fix = gmm.predict(X)",
"execution_count": 22,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.scatter(X[:, 0], X[:, 1], c=y_fix, marker='.')\nplt.axis('scaled');",
"execution_count": 23,
"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"
}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Get the average likelihood and BIC"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "stats(gmm, X)",
"execution_count": 24,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 24,
"data": {
"text/plain": "(-3244.0027264754044, -3313.0802792652257)"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now calculate these for GMMs with different numbers of identical components. Would expect likelihood to be the same, as the combined model is the same. However, BIC will decrease for models containing more parameters."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "k_try = range(1, 10)\nmodsel = np.array([stats(unit_gmm(k, dim), X) for k in k_try])",
"execution_count": 25,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(k_try, modsel[:, 0], label='logL')\nplt.plot(k_try, modsel[:, 1], label='BIC')\nplt.legend()\nplt.xlabel('k');",
"execution_count": 26,
"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"
}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Check I can match results for how stats vary with number of components in data and fit (where these match).\n\n**However, we can't really compare likelihoods based on different datasets, so the following tests probably aren't very illuminating.**"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def avg_fit_stats(k, d, N_obs, nsim=10):\n r = []\n for i in range(nsim):\n X, y = blobs(k, d, N_obs)\n r.append(stats(GaussianMixture(n_components=k, covariance_type='diag').fit(X), X))\n return np.mean(r, axis=0)",
"execution_count": 27,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "k_try = np.arange(1, 25)\nresults = np.array([avg_fit_stats(k, dim, N_obs) for k in k_try])",
"execution_count": 28,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(k_try, results[:, 0], label='logL')\nplt.plot(k_try, results[:, 1], label='BIC')\nplt.legend()\nplt.xlabel('k');",
"execution_count": 29,
"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"
}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "How do stats vary with number of dimensions?"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "k = 3\nd_try = np.arange(1, 10)\nresults = np.array([avg_fit_stats(k, d, N_obs) for d in d_try])",
"execution_count": 30,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(d_try, results[:, 0], label='logL')\nplt.plot(d_try, results[:, 1], label='BIC')\nplt.legend()\nplt.xlabel('d');",
"execution_count": 31,
"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"
}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "How do stats vary with number of dimensions and components in data and fit (where these all match)?"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "x_try = range(1, 25)\nresults = np.array([avg_fit_stats(x, x, N_obs) for x in x_try])",
"execution_count": 32,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(x_try, results[:, 0], label='logL')\nplt.plot(x_try, results[:, 1], label='BIC')\nplt.legend()\nplt.xlabel('k, d');",
"execution_count": 33,
"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"
}
}
]
}
],
"metadata": {
"kernelspec": {
"name": "conda-env-physcomp-py",
"display_name": "Python [conda env:physcomp]",
"language": "python"
},
"hide_input": false,
"language_info": {
"name": "python",
"version": "3.8.3",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"gist": {
"id": "",
"data": {
"description": "Testing that the likelihood of a GMM doesn't depend on the number of components",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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