{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting started" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial, we will do parameter inference on a simple statistical model. In total, this tutorial has an expected run time of 5 minutes. \n", "\n", "First off, let's see whether `delfi` is installed properly:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.8.0\n" ] } ], "source": [ "import delfi\n", "print(delfi.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "No error was raised, and we can continue." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the purpose of this example, we will consider a very simple statistical model, with a single parameter $\\theta$. Depending on $\\theta$, data is generated according to: $x|\\mathbf{\\theta} \\sim 0.5 \\mathcal{N}(x|\\mu=\\theta, \\sigma^2=1) + 0.5 \\mathcal{N}(x|\\mu=\\theta, \\sigma^2=0.1)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This model is implemented in `delfi.simulator`, we will import the model and create an instance:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from delfi.simulator import GaussMixture\n", "\n", "n_params = 1\n", "m = GaussMixture(dim=n_params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we will define a prior distribution over $\\theta$ as $\\mathcal{U}(-10, 10)$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import delfi.distribution as dd\n", "import numpy as np\n", "\n", "p = dd.Uniform(lower=[-10], upper=[10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary statistics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will not reduce the dimensionality of our data, and instead just apply the identity:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from delfi.summarystats import Identity\n", "\n", "s = Identity()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having defined the simulator, prior, and summary statistics, we instantiate a generator object:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from delfi.generator import Default\n", "\n", "g = Default(model=m, prior=p, summary=s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having specified the generator, we can draw parameters and data using the `gen()` method:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "21b5c02fe856447d95d1e811f447ced0", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=500.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0aa45711f169442cb46d8400d2a071e0", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=500.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "\n", "params, stats = g.gen(500)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 261, "width": 400 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(stats, params, '.')\n", "plt.ylabel(r'$\\theta$')\n", "plt.xlabel(r'x');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Inference" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Say, we observed data $x_\\text{o}$ and are interested in the posterior distribution $p(\\theta|x=x_\\text{o})$. The likelihood-free inference (LFI) algorithms implemented in `delfi` allow doing so, without using the likelihood function: In most real world application, the likelihood function is not available. We aim to do inference by just generating examples, i.e., simulating the model. \n", "\n", "We choose the toy model such that the posterior is easily tractable analytically. This will allow us to judge the result against the ground truth. We will carry out inference for $x_0 = 0$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "x0 = np.array([[0.]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic density estimation based LFI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A simple algorithm to use density estimation for LFI looks as follows:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](./basic.svg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$q_\\phi$ will be a mixture density network (MDN): The MDN is a neural network that maps from $x$ to a Gaussian mixture distribution. \n", "\n", "For our example, we will set $K=2$, such that the resulting mixtures will have two components." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To apply the above algorithm to the toy problem, create an instance of the inference algorithm specifying details:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "044b00b8e2af479e8a81eb902b12266f", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "922a6965269948e0bf25438556596d16", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "from delfi.inference import Basic\n", "\n", "inf_basic = Basic(obs = x0, generator=g, n_components=2, n_hiddens=[10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We specified that we want K=2 components, and the neural network got a single hidden layer with 10 units. Additional entries in the list passed for `n_hiddens` would create additional layers." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8c25e0e16737435cba521935ee2bdf27", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=4000.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "184932f23a12417a80cf1395cfcfc64d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=4000.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6a3775d777cb462180e9185242d5774d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=400000.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "logs, train_data, _ = inf_basic.run(n_train=4000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We drew `N=n_train` training examples and ran the algorithm. We can plot the loss function, across training rounds of the neural network:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 277, "width": 387 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "for i, l in enumerate(logs):\n", " plt.subplot(1, len(logs), i + 1)\n", " plt.plot(l['loss'])\n", " plt.xlabel('Iteration')\n", " plt.ylabel('Loss')\n", " plt.yscale('log')\n", " plt.title('Round {0}'.format(i + 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Say we observed $x_o = 0.$ and want to predict the posterior $\\hat{p}(\\theta | x=x_{\\text{o}})$:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "posterior = inf_basic.predict(x0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameters of the predicted posterior are:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "component 1: mixture weight = 0.59; mean = 0.09; variance = 0.82\n", "component 2: mixture weight = 0.41; mean = 0.02; variance = 0.10\n" ] } ], "source": [ "for k in range(2):\n", " print(r'component {}: mixture weight = {:.2f}; mean = {:.2f}; variance = {:.2f}'.format(\n", " k+1, posterior.a[k], posterior.xs[k].m[0], posterior.xs[k].S[0][0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The correct posterior for this problem is known -- since the prior is uniform it is simply: \n", "\n", "$$p(\\theta|x=x_{\\text{o}}) = 0.5 \\mathcal{N}(\\theta|\\mu=0, \\sigma^2=1) + 0.5 \\mathcal{N}(\\theta|\\mu=0, \\sigma^2=0.1)$$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 248, "width": 372 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "true_posterior = dd.MoG(a=[0.5, 0.5], ms=[[0.], [0.]], Ss=[[[1.0]], [[0.1]]])\n", "plt.plot(posterior.eval(np.arange(-5.0, 5.0, 0.01).reshape(-1,1), log=False), '-b')\n", "plt.plot(true_posterior.eval(np.arange(-5.0, 5.0, 0.01).reshape(-1,1), log=False), '-r')\n", "plt.legend(['predicted posterior', 'true posterior'], frameon=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Sequential Neural Posterior Estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the problem we picked here, the basic inference algorithm does a good job. More complicated problems, however, may require more sophisticated algorithms. \n", "\n", "Instead of sampling all parameters from the prior, we can use our simulator more efficiently by drawing only a first set of parameters from the prior and then switching to using a different distribution to sample from (a proposal distribution). Intuitively, the proposal distribution is chosen such that, when simulated, data is closer to $x_o$. In order to get the correct posterior, we will need to account for the fact that we drew these samples from a different distribution. There are three inference methods impelemented in delfi, each with a different approaches to this problem. APT or SNPE-C is the latest version of the SNPE algorithm and performs best on most problems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Automatic posterior transformation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Automatic Posterior Transformation (APT, sometimes referred to as SNPE-C) improves on SNPE-A and SNPE-B by adjusting for the difference between the proposal and prior during learing. This means that APT doesn't rely on post-hoc corrections or importance weights, which leads to more accurate inference than the previous two methods.\n", "\n", "This technique is described in \n", "\n", "> _Automatic Posterior Transformation for Likelihood-Free Inference_, by Greenberg, Nonnenmacher and Macke, ICML 2019." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "2e3712ac59fd41829c0f497d3cc49bff", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "4855f1f15b6145249a3c269744a8b607", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f49f7aa9268841ce93353829cfde5a06", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=2900.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "74a56dcb6619426485227c9e718e15ce", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=2900.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6c53531ebe0542abb9d91b8f399c7cbd", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "bab20107b226488a8ea18f5634597804", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "from delfi.inference import APT\n", "\n", "inf_APT = APT(obs=x0, generator=g, n_components=2, n_hiddens=[10])\n", "logs, train_data, posteriors = inf_APT.run(n_train=[3000, 1000], n_rounds=2, train_on_all=True)\n", "posterior = posteriors[-1]" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "component 1: mixture weight = 0.52; mean = 0.05; variance = 0.81\n", "component 2: mixture weight = 0.48; mean = -0.03; variance = 0.11\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 248, "width": 372 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for k in range(2):\n", " print(r'component {}: mixture weight = {:.2f}; mean = {:.2f}; variance = {:.2f}'.format(\n", " k+1, posterior.a[k], posterior.xs[k].m[0], posterior.xs[k].S[0][0]))\n", " \n", "true_posterior = dd.MoG(a=[0.5, 0.5], ms=[[0.], [0.]], Ss=[[[1.0]], [[0.1]]])\n", "plt.plot(posterior.eval(np.arange(-5.0, 5.0, 0.01).reshape(-1,1), log=False), '-b')\n", "plt.plot(true_posterior.eval(np.arange(-5.0, 5.0, 0.01).reshape(-1,1), log=False), '-r')\n", "plt.legend(['predicted posterior', 'true posterior'], frameon=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adapting to other problems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to use `delfi` with a specific problem, you'd need to implement a simulator class and possibly summary statistics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulators should inherit from a simulator base class. The base class for simulators specifies that each child needs to inherit a method called `gen_single()` -- the function that forward simulates a single $\\theta$ to data. It should return a dictionary that contains the result under a key called `data`. [This is also detailled in the docstring of the base class](https://github.com/mackelab/delfi/blob/master/delfi/simulator/BaseSimulator.py). For an actual implementation, you can see the code for the mixture model we used above: https://github.com/mackelab/delfi/blob/master/delfi/simulator/GaussMixture.py.\n", "\n", "For this example, we used the identity as a summary statistics. If you were to use summary statistics, consider the implementation of mean summary statistics for a basic example: https://github.com/mackelab/delfi/blob/master/delfi/summarystats/Mean.py, and again, there is a [base class specifying the interface](https://github.com/mackelab/delfi/blob/master/delfi/summarystats/BaseSummaryStats.py)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wright-Fisher" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "s = 0.01\n", "μ = 1e-6\n", "N = 100000" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "def simulation(N, s, μ, t, reps):\n", " p = np.empty((t[-1]+1, reps), dtype=float)\n", " p[0] = 0\n", " for i in range(1, t[-1]+1):\n", " p_ = p[i-1]\n", " p_ = (1 - μ) * p_ + μ * (1 - p_)\n", " p_ = p_ * (1+s) / (1 + p_ * s)\n", " p[i] = np.random.binomial(N, p_) / N\n", " return np.array([p[i] for i in t])" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "t = [0, 500, 1000, 2500, 5000] \n", "p = simulation(N, s, μ, t, 10)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 249, "width": 372 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(p, '-');\n", "plt.ylim(0, 1.01)\n", "plt.xlim(0, None);" ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [], "source": [ "class WFSimulator(delfi.simulator.BaseSimulator):\n", " def __init__(self, N, t, reps):\n", " self.N = int(N)\n", " self.t = t\n", " self.reps = reps\n", "\n", " def gen_single(self, params): \n", " s, μ = params\n", " try:\n", " p = simulation(self.N, s, μ, self.t, self.reps)\n", " except:\n", " print(\"params:\", params)\n", " raise\n", " return dict(data=p.ravel())" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 280, "width": 424 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "ax1.hist(np.random.normal(0.1, 0.1, 10000), bins=500, orientation='horizontal')\n", "ax1.axhline(s, color='r')\n", "ax2.hist(np.random.normal(1e-8, 1e-6, 10000), bins=500, orientation='horizontal')\n", "ax2.axhline(μ, color='r')\n", "fig.tight_layout()" ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f860d6ca403b4efea098cd80ef3d6f5b", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=500.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "5275bde3c9cd4ecfb80b87b0fdf9c562", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=500.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "model = WFSimulator(N, t, reps=10)\n", "prior = dd.Uniform([1e-4, 1e-10], [0.5, 1e-2])\n", "summary = Identity()\n", "gen = Default(model=model, prior=prior, summary=summary)\n", "params, stats = gen.gen(500)" ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [], "source": [ "x0 = simulation(N, s, μ, t, 10).ravel()" ] }, { "cell_type": "code", "execution_count": 136, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "12c8884756c5427d9c458a373991733a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "874bbca8f8cd403b970f286f885837e7", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a7f63da3b63b4c29991443bb7bacf335", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=2900.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "17bb6deaf202440e83be7667e313d883", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=2900.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8c2b2eb1c0134616b098e8190a59191b", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "df5e35ea6f304907bf5875d49acdb39b", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "inf_APT = APT(obs=x0, generator=gen, n_components=2, n_hiddens=[10])\n", "logs, train_data, posteriors = inf_APT.run(n_train=[3000, 1000], n_rounds=2, train_on_all=True)" ] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:delfi]", "language": "python", "name": "conda-env-delfi-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": "3.8.0" } }, "nbformat": 4, "nbformat_minor": 4 }