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March 15, 2020 03:44
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "h5aRsuwOBnFP" | |
| }, | |
| "source": [ | |
| "<span style=\"background-color:#12A7B9;padding: 5px 20px 5px 20px;line-height:30px;color:white;font-weight: bold; font-size: 24px; border-radius: 25px; margin: auto; width: 50%; display: block; text-align: center\">Approximate Inference: ABC \\& HMC</span>\n", | |
| "\n", | |
| "The goal of this assignment is to provide a replication of Section 5 of Turner and Van Zandt (2012) and offer a comparison between the Approximate Bayesian Computation - Sequential Monte Carlo (ABC SMC) and Hamiltonian Monte Carlo (HMC) algorithms under that toy example. The underlying focus is on a largely pedagogical application of the two methods, rather than the exploration of an intricate problem." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "sgF8b0r5BnFS" | |
| }, | |
| "source": [ | |
| "<span style=\"background-color:#12A7B9;padding: 5px 16px 5px 16px;line-height:24px;color:white; font-weight: bold; font-size: 18px; border-radius: 25px; margin: auto; width: 30%; display: block; text-align: center\">1. The Data</span>\n", | |
| "\n", | |
| "Section 5 of Turner and Van Zandt (2012) applies ABC SMC to synthetically-generated exponential data. The benefit of this example is that since the likelihood is known, we can take advantage of the conjugacy between the exponential and gamma distributions to compute the exact posterior, which will be Gamma distributed. Specifically,\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{aligned}\n", | |
| "p(\\theta) &= \\Gamma(\\alpha_0, \\beta_0) & \\text{(prior)} \\\\\n", | |
| "p(y|\\theta) &= \\text{Exp}(y|\\theta) & \\text{(likelihood)} \\\\\n", | |
| "p(\\theta|y) &= \\Gamma\\left(\\alpha_0 + n\\mid\\beta_0 +\\sum_{i=1}^n y_i\\right) & \\text{(posterior)}\n", | |
| "\\end{aligned}\n", | |
| "$$\n", | |
| "\n", | |
| "The authors generated a dataset of $n=500$ observations with $\\theta_{true} \\equiv \\lambda = 0.1.$ Furthermore, to compute the exact posterior they set the hyperparameters equal to $\\alpha_0 = \\beta_0 = 0.1.$\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 0, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-15T02:34:53.605922Z", | |
| "start_time": "2020-03-15T02:34:53.601048Z" | |
| }, | |
| "colab": {}, | |
| "colab_type": "code", | |
| "id": "FDWh24fsBnFU" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import scipy.stats as sts\n", | |
| "import seaborn as sns\n", | |
| "import matplotlib.pyplot as plt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 0, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-15T02:34:54.239054Z", | |
| "start_time": "2020-03-15T02:34:54.229028Z" | |
| }, | |
| "colab": {}, | |
| "colab_type": "code", | |
| "id": "z2Cb0bhPBnFY" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "N = 500 # Sample size\n", | |
| "RATE = 0.1 # True parameter value\n", | |
| "ALPHA0 = BETA0 = 0.1 # Hyperparameters\n", | |
| "SEED = 20200314\n", | |
| "np.random.seed(seed=SEED)\n", | |
| "\n", | |
| "likelihood = sts.expon(scale=1/0.1)\n", | |
| "data = likelihood.rvs(500)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-15T02:35:00.123139Z", | |
| "start_time": "2020-03-15T02:34:59.768087Z" | |
| }, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 265 | |
| }, | |
| "colab_type": "code", | |
| "id": "koNPsUWnBnFb", | |
| "outputId": "81da9820-1d42-4982-fb22-efbe45fe6701" | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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ELBg+5MVdBPvCo44zdPbjwF5V/a9hu6K+fhHxiUiWs5xM8FzDXoKh\nf4vTLCprV9WvqWqxqpYR/IxvVNVPEQO1i0iqiKSfXgY+AuwiBj4zqtoI1IrIBc6mlQRHJBh/7ZE+\nATEdHsCfAwcI9r/+U6TrCaHenwENwADBI4e7Cfa/vgocBF4BciJd51lqv5Lgn6w7gG3O489joX5g\nMbDVqX0XcJ+zfTbBMaOqgZ8D3kjXOsb7+CDwYqzU7tS43XnsPv3/aCx8Zpw6lwBVzufml0D2+dRu\nwyUYY0wcsG4cY4yJAxb2xhgTByzsjTEmDljYG2NMHLCwN8aYOGBhb4wxccDC3hhj4sD/BzMIKEDt\nILgpAAAAAElFTkSuQmCC\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "sns.distplot(data); plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "BsCjcKE2BnFg" | |
| }, | |
| "source": [ | |
| "<span style=\"background-color:#12A7B9;padding: 5px 16px 5px 16px;line-height:24px;color:white; font-weight: bold; font-size: 18px; border-radius: 25px; margin: auto; width: 30%; display: block; text-align: center\">2. Exact Posterior</span>\n", | |
| "\n", | |
| "I follow the update equation given above to compute the exact posterior. Both prior and posterior distributions are shown below." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 0, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-15T02:35:03.184965Z", | |
| "start_time": "2020-03-15T02:35:03.175987Z" | |
| }, | |
| "colab": {}, | |
| "colab_type": "code", | |
| "id": "8PmcEz13BnFh" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# Updated hyperparameters\n", | |
| "alpha = ALPHA0 + N\n", | |
| "beta = BETA0 + data.sum()\n", | |
| "\n", | |
| "# Exact posterior statistics\n", | |
| "true_mean = alpha/beta\n", | |
| "true_var = alpha/beta**2\n", | |
| "\n", | |
| "# Prior \n", | |
| "prior = sts.gamma(a=ALPHA0, scale=1/BETA0)\n", | |
| "\n", | |
| "# Exact Posterior\n", | |
| "true_post = sts.gamma(a=alpha, scale=1/beta)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-15T02:35:05.773321Z", | |
| "start_time": "2020-03-15T02:35:04.846005Z" | |
| }, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 354 | |
| }, | |
| "colab_type": "code", | |
| "id": "TisDdpIsBnFk", | |
| "outputId": "a64594d6-cc35-43a7-b04d-92b153605024" | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "True Posterior Mean\t: 0.10274\n", | |
| "True Posterior Variance\t: 0.00002\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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+AxyW1HOkM6trXzdrbbW1trVr8ylJF3snHgAAAALJltJaVTW0at74QU5HcVRY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\nzk7nnMZiR14jnYRCg39HJJLIk2NRXu7y/3i0lpY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| |
| "text/plain": [ | |
| "<Figure size 1152x360 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Samples\n", | |
| "prior_samples = prior.rvs(size=10000)\n", | |
| "post_samples = true_post.rvs(size=10000)\n", | |
| "\n", | |
| "# Text\n", | |
| "print('True Posterior Mean\\t: {:.5f}\\nTrue Posterior Variance\\t: {:.5f}'.format(true_mean, true_var))\n", | |
| "\n", | |
| "# Graph\n", | |
| "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,5))\n", | |
| "sns.distplot(prior_samples, ax=ax1, color=\"red\", label=\"Prior dist.\")\n", | |
| "sns.distplot(post_samples, ax=ax2, label=\"Exact posterior\")\n", | |
| "ax2.axvline(x=true_mean, label=\"True mean\", color=\"orange\")\n", | |
| "ax1.legend(); ax2.legend()\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "pBa23KwTBnFo" | |
| }, | |
| "source": [ | |
| "We can observe that the prior is very uninformative, with a lot of probability mass from the true parameter value. This distancing poses a difficulty for ABC if we choose the prior as our proposal distribution, which is usually the best choice given the knowledge available. An inaccurate proposal leads to high rejection rates. However, since we will be using SMC, which continually updates the proposal distribution, the problem is alleviated." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "63sP9YXRBnFp" | |
| }, | |
| "source": [ | |
| "<span style=\"background-color:#12A7B9;padding: 5px 16px 5px 16px;line-height:24px;color:white; font-weight: bold; font-size: 18px; border-radius: 25px; margin: auto; width: 30%; display: block; text-align: center\">3. HMC</span>\n", | |
| "\n", | |
| "Now, we assume that we do not have access to the exact posterior. Since the likelihood function is still available, we may use HMC to approximate the posterior distribution." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-14T03:08:21.659873Z", | |
| "start_time": "2020-03-14T03:08:02.958896Z" | |
| }, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| }, | |
| "colab_type": "code", | |
| "id": "22PGdxhbBnFq", | |
| "outputId": "256cea9d-56c6-4a83-fd6e-2e7a85a3e9fe" | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_0654f291125a70827c57b8b79d0836be NOW.\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "import pystan\n", | |
| "\n", | |
| "model = \"\"\"\n", | |
| "data {vector[500] y;} \n", | |
| "parameters {real<lower = 0.0> lambda;}\n", | |
| "model {\n", | |
| " lambda ~ gamma(0.1, 0.1);\n", | |
| " y ~ exponential(lambda);\n", | |
| "}\n", | |
| "\"\"\"\n", | |
| "stan_model = pystan.StanModel(model_code=model)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 223 | |
| }, | |
| "colab_type": "code", | |
| "id": "6GLddj5UB3De", | |
| "outputId": "5d74df04-1d47-463d-ea75-e522dede958f" | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Inference for Stan model: anon_model_0654f291125a70827c57b8b79d0836be.\n", | |
| "4 chains, each with iter=2000; warmup=1000; thin=1; \n", | |
| "post-warmup draws per chain=1000, total post-warmup draws=4000.\n", | |
| "\n", | |
| " mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat\n", | |
| "lambda 0.1 1.3e-4 4.6e-3 0.09 0.1 0.1 0.11 0.11 1349 1.0\n", | |
| "lp__ -1638 0.02 0.74 -1640 -1638 -1638 -1638 -1638 1480 1.0\n", | |
| "\n", | |
| "Samples were drawn using NUTS at Sun Mar 15 03:36:14 2020.\n", | |
| "For each parameter, n_eff is a crude measure of effective sample size,\n", | |
| "and Rhat is the potential scale reduction factor on split chains (at \n", | |
| "convergence, Rhat=1).\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "stan_results = stan_model.sampling(data = {'y' : data})\n", | |
| "print(stan_results)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 354 | |
| }, | |
| "colab_type": "code", | |
| "id": "7CpAE1DgE2Ur", | |
| "outputId": "8b412c09-d837-4554-871c-9f612e8ad74f" | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Approx. Posterior Mean\t: 0.10261\t Error\t: -0.127%\n", | |
| "Approx. Posterior Var.\t: 0.00002\t Error\t: 0.342%\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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gMg1sFji2Tu9YQrgdKcBiyDIUbSFQtVIaOVfvKE7lxGjoz0u9IDQZPP3hyGqd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\neEKVAAAAAElFTkSuQmCC\n", | |
| "text/plain": [ | |
| "<Figure size 576x360 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "HMC_samples = stan_results['lambda']\n", | |
| "# Text\n", | |
| "print('Approx. Posterior Mean\\t: {:.5f}\\t Error\\t: {:6.3f}%'.format(\n", | |
| " HMC_samples.mean(), 100*(HMC_samples.mean()/true_mean - 1)))\n", | |
| "print('Approx. Posterior Var.\\t: {:.5f}\\t Error\\t: {:6.3f}%'.format(\n", | |
| " HMC_samples.var(), 100*(HMC_samples.var()/true_var - 1)))\n", | |
| "\n", | |
| "# Graph\n", | |
| "fig, ax1 = plt.subplots(1,1, figsize=(8,5))\n", | |
| "sns.distplot(HMC_samples, ax=ax1, label=\"HMC\")\n", | |
| "sns.distplot(post_samples, ax=ax1, label=\"Exact posterior\")\n", | |
| "ax1.axvline(x=true_mean, label=\"True mean\", color='black')\n", | |
| "plt.legend(); plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "-v0J6DPUH3d1" | |
| }, | |
| "source": [ | |
| "HMC thus provides a very good approximation of the posterior distribution. Its estimates of both posterior mean and variance are very accurate.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "ishY6CAiBnFt" | |
| }, | |
| "source": [ | |
| "<span style=\"background-color:#12A7B9;padding: 5px 16px 5px 16px;line-height:24px;color:white; font-weight: bold; font-size: 18px; border-radius: 25px; margin: auto; width: 30%; display: block; text-align: center\">4. ABC SMC</span>\n", | |
| "\n", | |
| "Now, we further assume that the closed form of the likelihood is unknown or intractable. Turner and Van Zandt (2012) investigated the following three distance or similarity metrics:\n", | |
| "$$\n", | |
| "\\begin{aligned}\n", | |
| "\\rho_1(y_{sim}, y_{obs}) &= |\\bar{X} - \\bar{Y}| \\\\\n", | |
| "\\rho_2(y_{sim}, y_{obs}) &= |\\text{median}(X) - \\text{median}(Y)| \\\\\n", | |
| "\\rho_3(y_{sim}, y_{obs}) &= |\\text{IQR}(X) - \\text{IQR}(Y)|\n", | |
| "\\end{aligned}\n", | |
| "$$\n", | |
| "\n", | |
| "The code below provides an implementation of these three metrics and the SMC ABC algorithm with the thresholds `3, 1, 0.1, 1e-3, 1e-4, 1e-5`." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 0, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-14T10:42:53.266936Z", | |
| "start_time": "2020-03-14T10:42:52.539882Z" | |
| }, | |
| "colab": {}, | |
| "colab_type": "code", | |
| "id": "P5w5Qz5MQRDw" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import elfi\n", | |
| "\n", | |
| "def fn_simulator(theta, n_obs=N, batch_size=1, random_state=SEED):\n", | |
| " \n", | |
| " # Prepare for batching\n", | |
| " batched_theta = np.asanyarray(theta).reshape((-1, 1))\n", | |
| " \n", | |
| " # Simulate data\n", | |
| " y_sim = sts.expon.rvs(scale=1/batched_theta,\n", | |
| " size=(batch_size, n_obs), random_state=random_state)\n", | |
| " \n", | |
| " return y_sim" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 0, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-14T10:49:37.076822Z", | |
| "start_time": "2020-03-14T10:49:37.055878Z" | |
| }, | |
| "colab": {}, | |
| "colab_type": "code", | |
| "id": "0tGHllIsI91I" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def create_model(distance):\n", | |
| "\n", | |
| " m = elfi.new_model()\n", | |
| "\n", | |
| " # Specify the prior\n", | |
| " priors = []\n", | |
| " gamma_prior = elfi.Prior(prior, name='Gamma prior')\n", | |
| "\n", | |
| " # Simulate new data \n", | |
| " elfi.Simulator(fn_simulator, gamma_prior, observed=np.array([data]), name='Exponential')\n", | |
| " \n", | |
| " # Generate summary statistic and distance node\n", | |
| " if distance == 'mean':\n", | |
| " dist = elfi.Summary(lambda x: np.mean(x, axis=1), m['Exponential'], name='ss_mean')\n", | |
| " d = elfi.Distance('euclidean', dist, name='mean')\n", | |
| "\n", | |
| " elif distance == 'median':\n", | |
| " dist = elfi.Summary(lambda x: np.median(x, axis=1), m['Exponential'], name='ss_median')\n", | |
| " d = elfi.Distance('euclidean', dist, name='median')\n", | |
| " \n", | |
| " elif distance == 'IQR':\n", | |
| " dist = elfi.Summary(lambda x: np.subtract(*np.percentile(x, [75, 25], axis=1)), \n", | |
| " m['Exponential'], name='ss_IQR')\n", | |
| " d = elfi.Distance('euclidean', dist, name='IQR')\n", | |
| " \n", | |
| " else:\n", | |
| " raise(\"Metric invalid.\")\n", | |
| " \n", | |
| " return d\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "Kg4RTAjjQREA" | |
| }, | |
| "source": [ | |
| "__Reproducibility note__: the `.sample()` below fails out of the box due to dimensionality issues. I was unable to fix the problem via the API, so went the hacky way and created a very _ad hoc_ solution to this particular bug. The problem was contained in the `.rvs()` method of the `GMDistribution` class. The code modified is located at `elfi/methods/utils.py L227`. The change is:\n", | |
| "\n", | |
| "from: \n", | |
| "```\n", | |
| "x = rvs + perturb\n", | |
| "``` \n", | |
| "to: \n", | |
| "```\n", | |
| "x = rvs[0] + perturb\n", | |
| "x = x.reshape(-1, 1)\n", | |
| "```" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 0, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-14T13:27:54.586797Z", | |
| "start_time": "2020-03-14T13:27:54.582808Z" | |
| }, | |
| "colab": {}, | |
| "colab_type": "code", | |
| "id": "GEwBk_VfI98k" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "distances = ['mean', 'median', 'IQR']\n", | |
| "smc_results = dict()\n", | |
| "schedule = [3, 1, 1e-1, 1e-3, 1e-4, 1e-5]\n", | |
| "N = 500 # Target # of samples\n", | |
| "\n", | |
| "# For the three distances\n", | |
| "for distance in distances:\n", | |
| " \n", | |
| " # Create model, SMC object and sample.\n", | |
| " d = create_model(distance)\n", | |
| " smc = elfi.SMC(d, batch_size=20000)\n", | |
| " smc_results[distance] = smc.sample(N, schedule)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 0, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-03-15T03:10:44.213315Z", | |
| "start_time": "2020-03-15T03:10:42.014790Z" | |
| }, | |
| "colab": {}, | |
| "colab_type": "code", | |
| "id": "urYQ0bzWQREI", | |
| "outputId": "614772a5-776f-4844-cc17-5f4c2ea5430e", | |
| "scrolled": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Distance: mean\n", | |
| "------------------------------------------------------------------------------------------\n", | |
| "Threshold: 3e+00\t Approx. Posterior Mean\t: 0.10573\t Error\t: 2.911%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00019\t Error\t: 791.575%\n", | |
| "\n", | |
| "Threshold: 1e+00\t Approx. Posterior Mean\t: 0.10259\t Error\t: -0.149%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00002\t Error\t: -9.568%\n", | |
| "\n", | |
| "Threshold: 1e-01\t Approx. Posterior Mean\t: 0.10351\t Error\t: 0.747%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00001\t Error\t: -33.207%\n", | |
| "\n", | |
| "Threshold: 1e-03\t Approx. Posterior Mean\t: 0.10296\t Error\t: 0.216%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00002\t Error\t: -22.733%\n", | |
| "\n", | |
| "Threshold: 1e-04\t Approx. Posterior Mean\t: 0.10275\t Error\t: 0.011%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00002\t Error\t: -28.196%\n", | |
| "\n", | |
| "Threshold: 1e-05\t Approx. Posterior Mean\t: 0.10289\t Error\t: 0.142%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00001\t Error\t: -32.642%\n", | |
| "\n", | |
| "------------------------------------------------------------------------------------------\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
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\n", | |
| "text/plain": [ | |
| "<Figure size 864x360 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light", | |
| "tags": [] | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Distance: median\n", | |
| "------------------------------------------------------------------------------------------\n", | |
| "Threshold: 3e+00\t Approx. Posterior Mean\t: 0.09657\t Error\t: -6.008%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00017\t Error\t: 708.008%\n", | |
| "\n", | |
| "Threshold: 1e+00\t Approx. Posterior Mean\t: 0.09355\t Error\t: -8.943%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00003\t Error\t: 54.338%\n", | |
| "\n", | |
| "Threshold: 1e-01\t Approx. Posterior Mean\t: 0.09565\t Error\t: -6.899%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00002\t Error\t: 10.845%\n", | |
| "\n", | |
| "Threshold: 1e-03\t Approx. Posterior Mean\t: 0.09545\t Error\t: -7.099%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00003\t Error\t: 23.889%\n", | |
| "\n", | |
| "Threshold: 1e-04\t Approx. Posterior Mean\t: 0.09508\t Error\t: -7.456%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00003\t Error\t: 23.642%\n", | |
| "\n", | |
| "Threshold: 1e-05\t Approx. Posterior Mean\t: 0.09445\t Error\t: -8.072%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00003\t Error\t: 22.264%\n", | |
| "\n", | |
| "------------------------------------------------------------------------------------------\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 864x360 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light", | |
| "tags": [] | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Distance: IQR\n", | |
| "------------------------------------------------------------------------------------------\n", | |
| "Threshold: 3e+00\t Approx. Posterior Mean\t: 0.11436\t Error\t: 11.309%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00026\t Error\t: 1120.861%\n", | |
| "\n", | |
| "Threshold: 1e+00\t Approx. Posterior Mean\t: 0.11023\t Error\t: 7.286%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00004\t Error\t: 108.703%\n", | |
| "\n", | |
| "Threshold: 1e-01\t Approx. Posterior Mean\t: 0.11103\t Error\t: 8.072%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00003\t Error\t: 49.627%\n", | |
| "\n", | |
| "Threshold: 1e-03\t Approx. Posterior Mean\t: 0.11152\t Error\t: 8.547%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00004\t Error\t: 73.329%\n", | |
| "\n", | |
| "Threshold: 1e-04\t Approx. Posterior Mean\t: 0.11182\t Error\t: 8.836%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00004\t Error\t: 91.021%\n", | |
| "\n", | |
| "Threshold: 1e-05\t Approx. Posterior Mean\t: 0.11202\t Error\t: 9.032%\n", | |
| "\t\t\t Approx. Posterior Var.\t: 0.00004\t Error\t: 86.490%\n", | |
| "\n", | |
| "------------------------------------------------------------------------------------------\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 864x360 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light", | |
| "tags": [] | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Plot\n", | |
| "for distance in distances: \n", | |
| " print(f\"Distance: {distance}\\n\" + \"-\"*90)\n", | |
| " \n", | |
| " # Prepare figure\n", | |
| " fig, ax = plt.subplots(1, 1, figsize=(12, 5))\n", | |
| " \n", | |
| " # Get all samples for all thresholds\n", | |
| " all_samples = smc_results[distance].populations\n", | |
| " \n", | |
| " # Plot exact posterior\n", | |
| " sns.distplot(post_samples, ax=ax, label=\"Exact posterior\")\n", | |
| " \n", | |
| " # Go through all populations / thresholds\n", | |
| " for i, pop in enumerate(all_samples):\n", | |
| " \n", | |
| " # Retrieve samples\n", | |
| " samples = pop.samples['Gamma prior']\n", | |
| " \n", | |
| " # Print statistics\n", | |
| " print('Threshold: {:.0e}\\t Approx. Posterior Mean\\t: {:.5f}\\t Error\\t: {:6.3f}%'.format(\n", | |
| " schedule[i], samples.mean(), 100*(samples.mean()/true_mean - 1)))\n", | |
| " print('\\t\\t\\t Approx. Posterior Var.\\t: {:.5f}\\t Error\\t: {:6.3f}%\\n'.format(\n", | |
| " samples.var(), 100*(samples.var()/true_var - 1)))\n", | |
| " \n", | |
| " # Plot density curve for this population\n", | |
| " sns.distplot(samples, hist=False, ax=ax, label=\"{:.0e}\".format(schedule[i]))\n", | |
| " \n", | |
| " ax.set_xlabel(r\"Posterior Mean\")\n", | |
| " \n", | |
| " print(\"-\"*90)\n", | |
| " plt.legend()\n", | |
| " plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "KOtpLM-mQREQ" | |
| }, | |
| "source": [ | |
| "We can see that both the median and IQR provide systematically biased estimates of the posterior mean. The median overestimates whereas the IQR underestimates the mean. Furthermore, we can also observe that with $\\epsilon = 3$, all distances dramatically overestimate the variance of the posterior. Overall, the mean as a distance provides the best approximation to the posterior, at the cost of underestimating its variance by about 20-30%. Also note that the accuracy gains seems to marginal or not exist for $\\epsilon < 0.001$." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "7RlhF5KlQRET" | |
| }, | |
| "source": [ | |
| "<span style=\"background-color:#12A7B9;padding: 5px 16px 5px 16px;line-height:24px;color:white; font-weight: bold; font-size: 18px; border-radius: 25px; margin: auto; width: 30%; display: block; text-align: center\">5. Conclusion</span>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "P9zWSD8_QREW" | |
| }, | |
| "source": [ | |
| "This simple example demonstrates the importance of selecting an appropriate distance measure. Different measure may yield very different estimates of the posterior mean and variance. Whenever the closed form of the likelihood function is available, it is paramount to at least compare the performance of ABC with MCMC algorithms that provide asymptotic guarantees of unbiasedness.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "colab_type": "text", | |
| "id": "FX-DVTyoBnGb" | |
| }, | |
| "source": [ | |
| "<span style=\"background-color:#12A7B9;padding: 5px 16px 5px 16px;line-height:24px;color:white; font-weight: bold; font-size: 18px; border-radius: 25px; margin: auto; width: 30%; display: block; text-align: center\">6. References</span>\n", | |
| "\n", | |
| "Turner, B. M., & Van Zandt, T. (2012). A tutorial on approximate Bayesian computation. *Journal of Mathematical Psychology, 56*(2), 69-85." | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "collapsed_sections": [], | |
| "name": "Assignment 2.ipynb", | |
| "provenance": [] | |
| }, | |
| "kernelspec": { | |
| "display_name": "Python [conda env:capstone]", | |
| "language": "python", | |
| "name": "conda-env-capstone-py" | |
| }, | |
| "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" | |
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| "toc": { | |
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| "nav_menu": {}, | |
| "number_sections": true, | |
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| "skip_h1_title": false, | |
| "title_cell": "Table of Contents", | |
| "title_sidebar": "Contents", | |
| "toc_cell": false, | |
| "toc_position": {}, | |
| "toc_section_display": true, | |
| "toc_window_display": false | |
| }, | |
| "varInspector": { | |
| "cols": { | |
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| "lenVar": 40 | |
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| "kernels_config": { | |
| "python": { | |
| "delete_cmd_postfix": "", | |
| "delete_cmd_prefix": "del ", | |
| "library": "var_list.py", | |
| "varRefreshCmd": "print(var_dic_list())" | |
| }, | |
| "r": { | |
| "delete_cmd_postfix": ") ", | |
| "delete_cmd_prefix": "rm(", | |
| "library": "var_list.r", | |
| "varRefreshCmd": "cat(var_dic_list()) " | |
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| "types_to_exclude": [ | |
| "module", | |
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| } |
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