{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Variational API quickstart\n", "\n", "The variational inference (VI) API is focused on approximating posterior distributions for Bayesian models. Common use cases to which this module can be applied include:\n", "\n", "* Sampling from model posterior and computing arbitrary expressions\n", "* Conduct Monte Carlo approximation of expectation, variance, and other statistics\n", "* Remove symbolic dependence on PyMC3 random nodes and evaluate expressions (using `eval`)\n", "* Provide a bridge to arbitrary Theano code\n", "\n", "Sounds good, doesn't it?\n", "\n", "The module provides an interface to a variety of inference methods, so you are free to choose what is most appropriate for the problem." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import pymc3 as pm\n", "import theano\n", "import numpy as np\n", "\n", "np.random.seed(42)\n", "pm.set_tt_rng(42)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic setup\n", "\n", "We do not need complex models to play with the VI API; let's begin with a simple mixture model:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "w = pm.floatX([.2, .8])\n", "mu = pm.floatX([-.3, .5])\n", "sd = pm.floatX([.1, .1])\n", "\n", "with pm.Model() as model:\n", " x = pm.NormalMixture('x', w=w, mu=mu, sigma=sd, dtype=theano.config.floatX)\n", " x2 = x ** 2\n", " sin_x = pm.math.sin(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can't compute analytical expectations for this model. However, we can obtain an approximation using Markov chain Monte Carlo methods; let's use NUTS first. \n", "\n", "To allow samples of the expressions to be saved, we need to wrap them in `Deterministic` objects:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "with model:\n", " pm.Deterministic('x2', x2)\n", " pm.Deterministic('sin_x', sin_x)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [x]\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [204000/204000 03:06<00:00 Sampling 4 chains, 0 divergences]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 1_000 tune and 50_000 draw iterations (4_000 + 200_000 draws total) took 186 seconds.\n", "The estimated number of effective samples is smaller than 200 for some parameters.\n" ] } ], "source": [ "with model:\n", " trace = pm.sample(50000)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/dependencies/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", " FutureWarning,\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above are traces for $x^2$ and $sin(x)$. We can see there is clear multi-modality in this model. One drawback, is that you need to know in advance what exactly you want to see in trace and wrap it with `Deterministic`.\n", "\n", "The VI API takes an alternate approach: You obtain inference from model, then calculate expressions based on this model afterwards. \n", "\n", "Let's use the same model:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as model:\n", " \n", " x = pm.NormalMixture('x', w=w, mu=mu, sigma=sd, dtype=theano.config.floatX)\n", " x2 = x ** 2\n", " sin_x = pm.math.sin(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we will use automatic differentiation variational inference (ADVI)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:01<00:00 Average Loss = 2.2413]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 2.2687\n" ] } ], "source": [ "with model:\n", " mean_field = pm.fit(method='advi')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/dependencies/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", " FutureWarning,\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pm.plot_posterior(mean_field.sample(1000), color='LightSeaGreen');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that ADVI has failed to approximate the multimodal distribution, since it uses a Gaussian distribution that has a single mode.\n", "\n", "## Checking convergence" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on class CheckParametersConvergence in module pymc3.variational.callbacks:\n", "\n", "class CheckParametersConvergence(Callback)\n", " | CheckParametersConvergence(every=100, tolerance=0.001, diff='relative', ord=inf)\n", " | \n", " | Convergence stopping check\n", " | \n", " | Parameters\n", " | ----------\n", " | every: int\n", " | check frequency\n", " | tolerance: float\n", " | if diff norm < tolerance: break\n", " | diff: str\n", " | difference type one of {'absolute', 'relative'}\n", " | ord: {non-zero int, inf, -inf, 'fro', 'nuc'}, optional\n", " | see more info in :func:`numpy.linalg.norm`\n", " | \n", " | Examples\n", " | --------\n", " | >>> with model:\n", " | ... approx = pm.fit(\n", " | ... n=10000, callbacks=[\n", " | ... CheckParametersConvergence(\n", " | ... every=50, diff='absolute',\n", " | ... tolerance=1e-4)\n", " | ... ]\n", " | ... )\n", " | \n", " | Method resolution order:\n", " | CheckParametersConvergence\n", " | Callback\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __call__(self, approx, _, i)\n", " | Call self as a function.\n", " | \n", " | __init__(self, every=100, tolerance=0.001, diff='relative', ord=inf)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | flatten_shared(shared_list)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from Callback:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", "\n" ] } ], "source": [ "help(pm.callbacks.CheckParametersConvergence)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use the default arguments for `CheckParametersConvergence` as they seem to be reasonable." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:01<00:00 Average Loss = 2.2559]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 2.2763\n" ] } ], "source": [ "from pymc3.variational.callbacks import CheckParametersConvergence\n", "\n", "with model:\n", " mean_field = pm.fit(method='advi', callbacks=[CheckParametersConvergence()])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can access inference history via `.hist` attribute." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(mean_field.hist);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is not a good convergence plot, despite the fact that we ran many iterations. The reason is that the mean of the ADVI approximation is close to zero, and therefore taking the relative difference (the default method) is unstable for checking convergence." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 42.63% [4263/10000 00:00<00:00 Average Loss = 3.2279]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Convergence achieved at 4700\n", "Interrupted at 4,699 [46%]: Average Loss = 4.7996\n" ] } ], "source": [ "with model:\n", " mean_field = pm.fit(method='advi', callbacks=[pm.callbacks.CheckParametersConvergence(diff='absolute')])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(mean_field.hist);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's much better! We've reached convergence after less than 5000 iterations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another usefull callback allows users to track parameters. It allows for the tracking of arbitrary statistics during inference, though it can be memory-hungry. Using the `fit` function, we do not have direct access to the approximation before inference. However, tracking parameters requires access to the approximation. We can get around this constraint by using the object-oriented (OO) API for inference." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "with model:\n", " advi = pm.ADVI()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "advi.approx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Different approximations have different hyperparameters. In mean-field ADVI, we have $\\rho$ and $\\mu$ (inspired by [Bayes by BackProp](https://arxiv.org/abs/1505.05424))." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'mu': mu, 'rho': rho}" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "advi.approx.shared_params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are convenient shortcuts to relevant statistics associated with the approximation. This can be useful, for example, when specifying a mass matrix for NUTS sampling:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([0.34]), array([0.69314718]))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "advi.approx.mean.eval(), advi.approx.std.eval()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can roll these statistics into the `Tracker` callback." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "tracker = pm.callbacks.Tracker(\n", " mean=advi.approx.mean.eval, # callable that returns mean\n", " std=advi.approx.std.eval # callable that returns std\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, calling `advi.fit` will record the mean and standard deviation of the approximation as it runs." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [20000/20000 00:05<00:00 Average Loss = 1.9568]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 1.9589\n" ] } ], "source": [ "approx = advi.fit(20000, callbacks=[tracker])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now plot both the evidence lower bound and parameter traces:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16, 9))\n", "mu_ax = fig.add_subplot(221)\n", "std_ax = fig.add_subplot(222)\n", "hist_ax = fig.add_subplot(212)\n", "mu_ax.plot(tracker['mean'])\n", "mu_ax.set_title('Mean track')\n", "std_ax.plot(tracker['std'])\n", "std_ax.set_title('Std track')\n", "hist_ax.plot(advi.hist)\n", "hist_ax.set_title('Negative ELBO track');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that there are convergence issues with the mean, and that lack of convergence does not seem to change the ELBO trajectory significantly. As we are using the OO API, we can run the approximation longer until convergence is achieved." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [100000/100000 00:24<00:00 Average Loss = 1.8638]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 1.8422\n" ] } ], "source": [ "advi.refine(100000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16, 9))\n", "mu_ax = fig.add_subplot(221)\n", "std_ax = fig.add_subplot(222)\n", "hist_ax = fig.add_subplot(212)\n", "mu_ax.plot(tracker['mean'])\n", "mu_ax.set_title('Mean track')\n", "std_ax.plot(tracker['std'])\n", "std_ax.set_title('Std track')\n", "hist_ax.plot(advi.hist)\n", "hist_ax.set_title('Negative ELBO track');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We still see evidence for lack of convergence, as the mean has devolved into a random walk. This could be the result of choosing a poor algorithm for inference. At any rate, it is unstable and can produce very different results even using different random seeds.\n", "\n", "Let's compare results with the NUTS output:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "ax = sns.kdeplot(trace['x'], label='NUTS');\n", "sns.kdeplot(approx.sample(10000)['x'], label='ADVI');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we see that ADVI is not able to cope with multimodality; we can instead use SVGD, which generates an approximation based on a large number of particles." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [300/300 02:05<00:00]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with model:\n", " svgd_approx = pm.fit(300, method='svgd', inf_kwargs=dict(n_particles=1000), \n", " obj_optimizer=pm.sgd(learning_rate=0.01))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = sns.kdeplot(trace['x'], label='NUTS');\n", "sns.kdeplot(approx.sample(10000)['x'], label='ADVI');\n", "sns.kdeplot(svgd_approx.sample(2000)['x'], label='SVGD');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That did the trick, as we now have a multimodal approximation using SVGD. \n", "\n", "With this, it is possible to calculate arbitrary functions of the parameters with this variational approximation. For example we can calculate $x^2$ and $sin(x)$, as with the NUTS model." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# recall x ~ NormalMixture\n", "a = x**2\n", "b = pm.math.sin(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To evaluate these expressions with the approximation, we need `approx.sample_node`." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on method sample_node in module pymc3.variational.opvi:\n", "\n", "sample_node(node, size=None, deterministic=False, more_replacements=None) method of pymc3.variational.approximations.Empirical instance\n", " Samples given node or nodes over shared posterior\n", " \n", " Parameters\n", " ----------\n", " node: Theano Variables (or Theano expressions)\n", " size: None or scalar\n", " number of samples\n", " more_replacements: `dict`\n", " add custom replacements to graph, e.g. change input source\n", " deterministic: bool\n", " whether to use zeros as initial distribution\n", " if True - zero initial point will produce constant latent variables\n", " \n", " Returns\n", " -------\n", " sampled node(s) with replacements\n", "\n" ] } ], "source": [ "help(svgd_approx.sample_node)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(0.20617133)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_sample = svgd_approx.sample_node(a)\n", "a_sample.eval()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(0.23059109)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_sample.eval()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(0.01689826)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_sample.eval()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Every call yields a different value from the same theano node. This is because it is **stochastic**. \n", "\n", "By applying replacements, we are now free of the dependence on the PyMC3 model; instead, we now depend on the approximation. Changing it will change the distribution for stochastic nodes:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sns.kdeplot(np.array([a_sample.eval() for _ in range(2000)]));\n", "plt.title('$x^2$ distribution');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a more convinient way to get lots of samples at once: `sample_node`" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "a_samples = svgd_approx.sample_node(a, size=1000)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sns.kdeplot(a_samples.eval());\n", "plt.title('$x^2$ distribution');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `sample_node` function includes an additional dimension, so taking expectations or calculating variance is specified by `axis=0`." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(0.0963961)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_samples.var(0).eval() # variance" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(0.24696937)" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_samples.mean(0).eval() # mean" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A symbolic sample size can also be specified:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "i = theano.tensor.iscalar('i')\n", "i.tag.test_value = 1\n", "a_samples_i = svgd_approx.sample_node(a, size=i)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(100,)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_samples_i.eval({i: 100}).shape" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10000,)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_samples_i.eval({i: 10000}).shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unfortunately the size must be a scalar value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Converting a Trace to an Approximation\n", "\n", "We can convert a MCMC trace into an Approximation. It will have the same API as approximations above with same `sample_node` methods:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trace_approx = pm.Empirical(trace, model=model)\n", "trace_approx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then draw samples from the `Emipirical` object:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/dependencies/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", " FutureWarning,\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pm.plot_posterior(trace_approx.sample(10000));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multilabel logistic regression\n", "\n", "Let's illustrate the use of `Tracker` with the famous Iris dataset. We'll attempy multi-label classification and compute the expected accuracy score as a diagnostic." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/env/miniconda3/lib/python3.7/site-packages/sklearn/utils/validation.py:71: FutureWarning: Pass return_X_y=True as keyword args. From version 0.25 passing these as positional arguments will result in an error\n", " FutureWarning)\n" ] } ], "source": [ "from sklearn.datasets import load_iris\n", "from sklearn.model_selection import train_test_split\n", "import theano.tensor as tt\n", "import pandas as pd\n", "\n", "X, y = load_iris(True)\n", "X_train, X_test, y_train, y_test = train_test_split(X, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](http://5047-presscdn.pagely.netdna-cdn.com/wp-content/uploads/2015/04/iris_petal_sepal.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A relatively simple model will be sufficient here because the classes are roughly linearly separable; we are going to fit multinomial logistic regression." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " rval = inputs[0].__getitem__(inputs[1:])\n", "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " rval = inputs[0].__getitem__(inputs[1:])\n" ] } ], "source": [ "Xt = theano.shared(X_train)\n", "yt = theano.shared(y_train)\n", "\n", "with pm.Model() as iris_model:\n", " \n", " # Coefficients for features\n", " β = pm.Normal('β', 0, sigma=1e2, shape=(4, 3))\n", " # Transoform to unit interval\n", " a = pm.Flat('a', shape=(3,))\n", " p = tt.nnet.softmax(Xt.dot(β) + a)\n", " \n", " observed = pm.Categorical('obs', p=p, observed=yt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Applying replacements in practice\n", "PyMC3 models have symbolic inputs for latent variables. To evaluate an espression that requires knowledge of latent variables, one needs to provide fixed values. We can use values approximated by VI for this purpose. The function `sample_node` removes the symbolic dependenices. \n", "\n", "`sample_node` will use the whole distribution at each step, so we will use it here. We can apply more replacements in single function call using the `more_replacements` keyword argument in both replacement functions.\n", "\n", "> **HINT:** You can use `more_replacements` argument when calling `fit` too:\n", "> * `pm.fit(more_replacements={full_data: minibatch_data})`\n", "> * `inference.fit(more_replacements={full_data: minibatch_data})`" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "with iris_model:\n", " \n", " # We'll use SVGD\n", " inference = pm.SVGD(n_particles=500, jitter=1)\n", " \n", " # Local reference to approximation\n", " approx = inference.approx\n", " \n", " # Here we need `more_replacements` to change train_set to test_set\n", " test_probs = approx.sample_node(p, more_replacements={Xt: X_test}, size=100)\n", " \n", " # For train set no more replacements needed\n", " train_probs = approx.sample_node(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By applying the code above, we now have 100 sampled probabilities (default number for `sample_node` is `None`) for each observation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we create symbolic expressions for sampled accuracy scores:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "test_ok = tt.eq(test_probs.argmax(-1), y_test)\n", "train_ok = tt.eq(train_probs.argmax(-1), y_train)\n", "test_accuracy = test_ok.mean(-1)\n", "train_accuracy = train_ok.mean(-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tracker expects callables so we can pass `.eval` method of theano node that is function itself. \n", "\n", "Calls to this function are cached so they can be reused." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "eval_tracker = pm.callbacks.Tracker(\n", " test_accuracy=test_accuracy.eval,\n", " train_accuracy=train_accuracy.eval\n", ")" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [100/100 00:38<00:00]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " rval = inputs[0].__getitem__(inputs[1:])\n", "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " rval = inputs[0].__getitem__(inputs[1:])\n" ] } ], "source": [ "inference.fit(100, callbacks=[eval_tracker]);" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nOydd3hb1fnHP0eSLcl7JY6znEAGI2GGEFJC2IRlVtikhTJCW2gLpSW0hYb1a8sse5QZNoUADnsFMiAhCYTs6UzbifeSLdmSzu+PV9eSFXkksWw5vt/n0SPp6urec8+95/2+7/c9Q2mtMWHChAkTvReW7i6ACRMmTJjoXphEYMKECRO9HCYRmDBhwkQvh0kEJkyYMNHLYRKBCRMmTPRymERgwoQJE70cJhGY2GeglPpEKfWrzt7XhIl9HcocR2CiO6GUqgv5mgB4AF/g+1St9WtdX6o9h1LqeOBroB7QQBHwL631i91ZLhMm2oKtuwtgondDa51kfFZKbQau0Vp/Gb6fUsqmtfZ2Zdn2AkVa64FKKQWcA7yjlFqotV4VulNnXlPgXEpr7e+M45noXTClIRMxCaXU8Uqp7UqpW5VSO4AXlVLpSqkPlVKlSqnKwOeBIf/5Ril1TeDzlUqpeUqpBwL7blJKnb6H+w5VSs1RStUqpb5USj2hlHq1vWvQgveBSuCgwHnmK6UeVkqVA9OVUqlKqRmBa9qilPq7UsoSOK9VKfWgUqosUKYblFJaKWULuYZ7lVLzkQhkP6XUAUqpL5RSFUqptUqpi0Ku4wyl1KrAdRQqpW4JbM8K1GVV4H9zjTKY6B0wb7aJWEY/IAPIBa5DntcXA98HAw3A4238/2hgLZAF3Ac8H/Ccd3ff14EfgExgOjClI4VXSlmUUucBacDykPMUANnAvcBjQCqwHzAR+CVwVWDfa4HTgcOAI4BzI5xmClI3yUAp8EWgvH2BS4AnlVIHBfZ9HpHbkoFRiIQF8CdgO9AnUK6/IrKWiV4CkwhMxDL8wD+01h6tdYPWulxr/a7Wul5rXYsY0olt/H+L1vq/Wmsf8DKQgxi6Du+rlBoMHAXcobVu1FrPA/LbKXd/pVQVUAb8A5iitV4b+K1Ia/1YQBJqRIz1bVrrWq31ZuBBgkRzEfCI1nq71roS+FeEc72ktV4ZON4kYLPW+kWttVdr/RPwLnBhYN8mJDJJ0VpXaq1/DNmeA+RqrZu01nO1mTzsVTCJwEQso1Rr7Ta+KKUSlFLPBCSUGmAOkKaUsrby/x3GB611feBj0m7u2x+oCNkGsK2dchdprdO01hla68O01m+28t8sIA7YErJtCzAg8Ll/2P6Rzhu6LRc4OiDxVAXI6HIksgK4ADgD2KKU+lYpdUxg+/3ABuBzpVSBUmpaO9dnYh+DSQQmYhnhXumfgJHA0VrrFOC4wPbW5J7OQDGQoZRKCNk2aC+OF3pNZYg3nhuybTBQGHLugSG/RTpv6PG2Ad8GSMh4JWmtfwOgtV6ktT4HkY3eB94ObK/VWv9Ja70fkAfcrJQ6ac8v0URPg0kEJnoSkpG8QJVSKgORXaIKrfUWYDGS2I0PeNFnd9KxfYgxvlcplayUygVuBoxE9NvAH5RSA5RSacCt7RzyQ2CEUmqKUiou8DpKKXVgoOyXK6VStdZNQA0ivaGUOkspNSyQE6lGuu+avY96EUwiMNGT8B/AiXjSC4BPu+i8lwPHAOXAPcBbyHiHzsCNgAtJIM9DEr0vBH77L/A5sAz4CfgY8BIcZ9ECgbzJqUjeoQiRu/4N2AO7TAE2B2S16wPXBTAc+BKoA74HntRaz+6k6zPRA2AOKDNhYjehlHoLWKO1jnpEEnbe04Gntda57e5swsRuwIwITJhoBwF5Zf9Ad9BJyCCx97vgvM5A33+bUmoAIoW9F+3zmuh9MInAhIn20Q/4BpFOHgV+E+iaGW0o4E5kQNpPwGrgji44r4leBlMaMmHChIleDjMiMGHChIlejh436VxWVpYeMmRIdxfDhAkTJnoUlixZUqa17hPptx5HBEOGDGHx4sXdXQwTJkyY6FFQSm1p7TdTGjJhwoSJXg6TCEyYMGGil8MkAhMmTJjo5TCJwIQJEyZ6OaJKBEqpSYFVkjZEmto2sFLT0sBrXWDaXBMmTJgw0YWIWq+hwBzxTwCnIKsfLVJK5Yeu26q1vilk/xuBw6NVHhMmTJgwERnRjAjGAhu01gVa60bgTWSOltZwKfBGFMtjwoQJEyYiIJpEMICWqydtJ7jyUgsE5mEfSnAN1fDfr1NKLVZKLS4tLe30gpowYcJEKGbNgsLC9vfbVxAryeJLgHcCC3XsAq31s1rrMVrrMX36RBwYZ8KECROdAq3h/PPh6ae7uyRdh2gSQSEtl9YbSHAJvnBcgikLmTBhIgbQ2AheL7hc3V2SrkM0iWARMFwpNVQpFY8Y+/zwnZRSBwDpyMpIJkyYMNGt8ATWnnO7u7ccXYmoEYHW2gvcAHyGzKP+ttZ6pVLqLqVUXsiulwBvanM+bBMmTMQADALoTUQQ1UnntNYfI+ushm67I+z79GiWwYQJEyZ2B72RCGIlWWzChAkTMQGTCEyYMGGil8PMEZgwYcJEL4dBAAYh9AaYRGDChAkTIeiN0lCPW6HMRPegqgo2b4bDDmu5vbERFi+G8eO7pVi9Eh99BGVl8jkuDvLyICmpe8u0u1i2DAYOhIyM7i7JruiNRGBGBCY6hEcegeOO23X7u+/CL34BRUVdX6beiM2b4ayz4Mor5XX55fDKK91cqD3ACSfAww93dykiw8wRmDDRCioqoLZWRlyGbweoqen6MvVGVFfL+1NPwerVLbf1FGgNlZXyPMUizIjAhIlWYDSKhoaW243vvanRdCeMes7NhZEj5XP4PelMzJ8PU6aA3995x2xqEjJoauq8Y3YmTCIwYaIVGMamNSLoTT0suhNGfTudoBQ4HNElgi+/hFdf7dx5dwwDGx5dxgpMIjBhohWYRBAbMOrb4ZB3pzO6RNBaJNgZx4xVIjBzBCZMtAJTGooNGPXsdAbfexoRGIY2VokgNCLoLTOgmURgokNozeD3xsE33YlQach47woiqK/v/GPGeo7A749dsupsmERgokMwI4LYgFHPodJQNOu+N0pDofXZW55rkwhMdAhmjiA2EB4RRDtZHM2IwCSC2IFJBCY6hN5EBIWFndtdsjPR1cni1u773iDWiSD0WTaJwISJEPQWaai8HPbbD95/v7tLEhn7QrK4p+QIwj/vyzCJwESH0FsigvJymT+ppKS7SxIZDQ1gs8kLenayOFYjApMITJhoBe0Rwb7SYIzriVVvtaEhKAtBz44ITCKIHZhEYKJDaE8a2lciAuN6YtlIGbIQmBFBNGDmCDoZSqlJSqm1SqkNSqlprexzkVJqlVJqpVLq9WiWx8Sewe9vfbTlvjaOINaJoKGhe4jAzBHs24jaegRKKSvwBHAKsB1YpJTK11qvCtlnOHAb8AutdaVSqm+0ymNizxFq5Pd1aagnGKlwaSiadW/c394UEbjdsr5DXd2+81y3h2hGBGOBDVrrAq11I/AmcE7YPtcCT2itKwG01jGaouvdCDX+pjTUvWgtIojWVAi9NUeQlhb83BsQTSIYAGwL+b49sC0UI4ARSqn5SqkFSqlJUSyPiT1ER4hgX2kwPS1Z7HCIdBet8vZGIvB4IDVVPu8rz3V76O6lKm3AcOB4YCAwRyk1WmtdFbqTUuo64DqAwYMHd3UZez1CG0OoQfD5pKslmBFBVyFSshik3PHx0Tkf9L65hrKygp97A6IZERQCg0K+DwxsC8V2IF9r3aS13gSsQ4ihBbTWz2qtx2itx/Tp0ydqBTYRGa1FBKGNZF8jglg1UpGkIWN7Z8PvDxJ9b4oITGmoc7EIGK6UGqqUigcuAfLD9nkfiQZQSmUhUlFBFMtkYg/QGhG0Rgo9GbEeEUQaR2Bs72yEkntvSxabRNBJ0Fp7gRuAz4DVwNta65VKqbuUUnmB3T4DypVSq4DZwJ+11uXRKpOJPUNr0lDoZzMi6Bq0JQ11NtrKDe0NYl0aMnMEnQyt9cfAx2Hb7gj5rIGbAy8TMQrDCFgsrfexbqvBaA1PPAG//CWkpESnjJ2FnhARdBURtOYAdNZxY7WOje6jVuu+4+C0B3NksYl2YTTc9PQ9iwjWrIEbb4T8cGEwBtETjFRXSUOhRNBbpCGtg3XscPSeiMAkAhPtwjAyrRGB3d42EdTWtnyPZcS6NNRaRBANg9UbIwIjOW4SgQkTYTCMQEZGZCJIS2u7wdTVtXyPZcSyNKR15HEEEN2IICmp93QfDV0BziQCEyZCYDSGtoigrYjA5ZL3nkQEsWikmpqEDLo6WRx+3/cWsRwRGM+x3W4SgQkTLdCeNJSe3rGIwCCEWEYsRwThy1SGfo5mRBB+3zvruF5v9KbG2FOYEYEJE62gI9KQGRFEH+HLVELXEUE0pCGIvSVBTSIwYaIVuN2glPStjtRltD0iMHMEnYPwZSpDP0eTCDIy5P52ltEOfYZijXBNIjDRa3HbbXDrra3/biQonU6ZX8hovOHSUGthfk+MCGKRCLpTGurMc4Qa11ir596aI+juSedMxABmz25bqw0lAuN7XFxLaQiEICJNfNaTIoJY7tESSRqKj5doLdoRgXH+xMTOOy7EHhGERwRVVW3vv6/AjAhMUFfXtpE2pjUI9z7DiaA178mMCDoHkaQhpaK3OE1obgg6L0/gdovHDbFXz6Y0ZKLXwuVqu0ePMYgpEhHYbJCQIN9byxP0pIigJySLQ4kAxGD1FGnIGLmbnCzfY62eQ4nAbjeJwEQvQkcignBpyHh3OoNSRWtEYEYEnYNQIxWKaK1bHEka2lt4vZJ0TkoKfo8lmDkCE70WLlf7OYLWIgKnMxjmt9ZozIigc9BaRBBNIrBag957Z0hDhqGNVSLordKQSQS9HD5f0Ij4fNLwwxEpWWy870sRgdcbNEyxZqAgcrIYoksEDkdQ+uuMc4ROWwGxV8+9lQhMaaiXI9TLay1PEJ4sNhqHsb2jEYHHE5uetoFQQxeL5YyULDa+R5MIjPN1RkRgXENPyBGYRGCi1yDUS2/NYw/3/FuThtqLCMI/xxpCjWmsearQ9dKQcX97U0RgPMMGEfh8sVfGaMAkgl6OjhjpvZWGOkI2sQDDSCkVm42/u6Shzhy0FutEYJTPSBaHbtuXYRJBL0dHjHRb4wg6Ig25XJCV1fY5YgHGdSUnx55kAd3Tayha0lAsE4HFIt2iTSIw0WvQ0YigNSIw+ltD2xFBdnbwc6wilAhizUCBlM9uF0MVimhp2dFMFsdyjsDhkKjQJAITvQYdjQg6Ig1FajCNjdLY+/Vr+xyxAOO6UlJiz0DBrstUGjAjgs5DaB2bRNBJUEpNUkqtVUptUEpNi/D7lUqpUqXU0sDrmmiWx8Su2NuIoL1ksXFMMyLYe4QvU2kg2kQQFyfdintDjsDjCT7PvYkIojaOQCllBZ4ATgG2A4uUUvla61Vhu76ltb4hWuUw0TbaiwiMvvWhEtDuJIsNIjAigp7QaygpKTYjgvBlKg1Es9dQZmZwPqPeQARmRND5GAts0FoXaK0bgTeBc6J4vh6B/Hx48MHuLkUQ7UUEoX3XDd10d8YRGOTSkyKClJTYXT2rrYigs8sbahSdzuhIQ7FGuCYRdD4GANtCvm8PbAvHBUqpZUqpd5RSgyIdSCl1nVJqsVJqcWlpaTTK2mWYMQMeeqi7SxFEexFBeN/1UM9wd6ShnpQjMBKZPl/3lSUS2pKGoO3FgfYEoUYxIaH3RgSdXa+xiO5OFs8ChmitDwG+AF6OtJPW+lmt9Rit9Zg+ffp0aQE7G9XVUFHR3aUIor2IILzvukEExgI17SWLe1JEYJQ/JUXeY81ItSUNGb93JroiIoi1Ou6tOYJoEkEhEOrhDwxsa4bWulxrbfDtc8CRUSxPTKC6Wh6sWHm46urE20tMjGykw6c1MIggNFKw2aRLY1sRQXq6LKISy0QQHhHEmpFqSxqC6BJBb44IYqWtRhPRJIJFwHCl1FClVDxwCZAfuoNSKifkax6wOorliQnU1Mh7ZWX3lsOAyyUkkJjYdkTQGhGENppIRGAY/sREafw9gQiMiCDW9OvWpKFoGaxoRgSxPo4AehcRRK3XkNbaq5S6AfgMsAIvaK1XKqXuAhZrrfOB3yul8gAvUAFcGa3yxAqqq+W9shJyctretytQVycGWqm2I4JwaSicIFpbxMM4ZlJSzyGCnuCthiIaEYHWLYknIQFqa/f+uMbIXeM6YrmOTSLoJGitPwY+Dtt2R8jn24DbolmGWINBBLGSJzAiAqX2LCIIJYK2pKGeEhHY7cF1l2PNW20vWdyZRNDYKO+hDkBJyd4fN3RsAsQeEXg8JhGYiDKamoKNNVakofYigkjJ4qqqXXMH7UlDPSUicDgk5wGxZ6S6MlkcKRLsLGkolus4dD1lkwhMRAVGNACxQwTtRQSRDP7uSEMul0gBdnvPIAKnM+itxlpE0JXJ4nAi6MxkcWhEEIt13Bsjgu7uPtqrYCSKIXakISMiaM1Id1QaaisiMCKOnkIEseqtdqU01JsjAuOajd5wvYEIzIigC9ETI4LWxhHsTkSQmCifY50IDI87FvVrv7+lfh2KnhgRxCoRhNZx+Ej6fRkmEXQhYpEIOtpraE+TxcbxIfaJIDwiiCXZwqjbrooIWnMAtJZnZU8Ry0SgdcscAfQeIjCloS5ELBJBtMcR9KSIIDxHEEtGqrVlKmHXJUQ7A5EcgNDte3PcUCKIJbIN7yllfDaJwESnwiCClJTYyBFoLYbayBG4XCJBhKIzxhGERgSRzhEriOWIoLXVyaDzjHRb5+usxWkMIrBY5BVLZBupjk0iMNHpMJLFQ4fGRkRghPpGRGBsC9/Hag16yU6n/McgtY6MIwiNCIyBSrGInhoRdFWyGPY+YRyejI2lOjaJwESXwDCeubmxQQThffxDtxkI77tufDbKH9prqL2IwCCEWJWHwscRxFJE0NrC9SDEZbFEP1kcWo69OW6sEoHhyJg5AhNRRXW1PFjZ2bFBBKGjfg0jHZ4nCO+7bnwOJ4KORgQQ20QQq91HwzX7UHTmwjEGIiWLQ7fvKUKJIC4utsi2N0cEZq+hLkR1NaSmQkaG5Aj2tgfG3iI0IjDKESkiiEQEFRUyFYOxkHp74wiM80DsrlIWywPK2pKGjO1dERGY0tC+CTMi6ELU1EiiOD1djExnDNDZG3QkIgiXhkKJINQodXQcAcRuRGBEP7EYEbQlDUH0iCC819C+LA2ZRGCiS2BEBOnp8r275aGO5Ahak4YiEUF4RODzyf/DI4JYJYJYTha3JQ0Z23tCsjh0wFasEUGkHEFrDs6+BpMIuhCh0hDEDhG0FxG0RgThnlNTU8uuoaERB8Q2ETQ1CXHFavfRWJGGzBzBnqOsDGbN6pxjdTZMIuhChEcE3T2WwDDU7UUEHZWGoGVUEBpxhL7HIhGEGtpYjghak4Y6W8IwjmVMyd0ZEYHXK69YjQiiTQRPPgl5ed3f7iPBJIIuRKxKQ3sSEVRXt9weaaHvnhQRhC+9CbHlrXZ1RGDkhoxOBJ0RERjPRm8lgoICed+ypXOO15kwiaALEZoshu4ngo5EBOFEECk6gGBEENpoemJEEKvz4HSHNBTpXu/NOcINbawRQThRGZ87iwgMAohFIjC7j3YR/H5Z6i9WcwSG5xdpHEFrxr89aSg8InA6W5/crrsRSRqKpYigPWkoGkQQ6V7vjTQUfg2xmiOI1oCyWCYCMyLoItTWyriB1FRZuNti6X6t0OWSh95mk2kkHI6OjyMI/xxpEY/wiCCW1ySIJA3Fkrfa0CD1Z2j24Yh2RGC3y/n35YigNWnI65WOBHsDnw+2bZPPvY4IlFKTlFJrlVIblFLT2tjvAqWUVkqNiWZ5uhPG9BKpqUICaWmxEREY3jpEnoG0tXEE4Z87EhFA7BJBaPfMWEwWh2v24Yg2ERijlzszIugpRACRB0vuDoqLg9faq4hAKWUFngBOBw4CLlVKHRRhv2TgD8DCaJUlFhA68yhInqC7icCYedRAJCPdmkQQ/rkjvYZaO0csINaTxa0tU2kg2kQAe784Tbj0EmtE0FqOAPZeHjKMf3x8LyMCYCywQWtdoLVuBN4Ezomw393Av4F9etiGMfNoaqq8Z2R0PxG0FxEYM4WGGqD4+KBX2p401JMigljvPtraMpUGotVrqDPP0RNyBBZL0BGAzieCo4/ufUQwANgW8n17YFszlFJHAIO01h+1dSCl1HVKqcVKqcWlpaWdX9IuQKg0BBIRxEKOoC1vvbFRyCCSRAC7ashgRgTRQiTDHApjrqfOWuuhtYhgX5eGwq+5s4lgwgQZWBZr8211W7JYKWUBHgL+1N6+WutntdZjtNZj+vTpE/3CRQGRiCDWI4LWpjUIn3YgdFukiCB0v1gnAkOHt1pjz0i1FxHA3mvZbZ2vsyOC3kYEmZlwUEAc37p1747X2YgmERQCg0K+DwxsM5AMjAK+UUptBsYB+ftqwjgWiaC9iKC1vuvhE5FB6xFBYmJwhtJI54gVhF+rzRZ7EUFHiKCz5KFIRrE3JIujSQS5ufIyvscSokkEi4DhSqmhSql44BIg3/hRa12ttc7SWg/RWg8BFgB5WuvFUSxTtyE8WWzkCLTuvjJ1NCKIZBBC36H1XkOhx4eeRQSxbqRC0RVE0FnJ4ljNEXg8LccQQPSIYPPmvTteZyNqRKC19gI3AJ8Bq4G3tdYrlVJ3KaXyonXeWEVNjcgNxlD99HTpW1xb231l6syIoLVxBKHHj3SOWEH4tTYbKb8/JtbWNCOC6CNaEYHWQSLo31+uu82IoKmpyxmyXSJQSmUrpZ5XSn0S+H6QUurqjhxca/2x1nqE1np/rfW9gW13aK3zI+x7/L4aDUBwniGjx00sTDPRXkTQ2hz4exQR7NwJ69bFLBG0aqR27oTVq7utXAbaSxZ3NhFEOl9nRwTNdez3Qwx0AmmTCDYW7vqHDqJ87irq64UIrFYYOLAdIli3rsu1o45EBC8hXn3/wPd1wB+jVaB9FQYRGOhuItC69YjAkKtaSxbvUUSwaRMUFJDk9NHUJD2SYgnhA7bi4gJGqqBAunl0oobX0LD70kBHk8XRjggaGvQe10WrRFBdDcuWdftD0SYRbNm5Z+XzeNjyUzkQlIVyc9uw8263PBxlZbt/rr1AR4ggS2v9NuCHZslnLwdc9wJoDVVVzV+rq4P5AejAfEPr10eVJTwekabCIwK/P+jV722yuDkiqK9vTogk6rrm32IJ4dKLzQZN9U2i6fn9nTrH8333wSGH7J5d6Q5paJf77tDU13j32HtvNUdQVgbl5fLqRoQummOgmQhc3mCib3dQVcWWYmkcHSKCoiJ5+Kqq9n5ei91AR4jApZTKBDSAUmocsAc10ougNaxZA/PnNxvz1iKCiGMJtJaJSbZti/Bj5yB05lED4WsKtycNdWQcQVISUFIiMXFKCkn1Jc2/xRLCDW1cHHhr6oODCjpxXdEffpDc0Lp1u1e+9sYRGPvtLYy5dXaRhrw1NLgV7NixR8d1uyXiMgbsNUcEhYXSt7Kbu9K43RGSxRZha7ctWWTC3UVhIVvqxOvLzZKGlZsr9n4XR8DrhY0bZf4Z6NJG0hEiuBnp7bO/Umo+MAO4Maql6skwSKCgQGaXW74cfD5qatqWhubNg9/8JtAwGhrEohYXRy1pFDrzqAHjs/Fbq+MI7CINOHXQOFos0sDDxxEkJWkJdZOTweEgiboW5+gQvF5YsqRFhNXZCDe0NpumqaY+mNjpxKz+ihUt3zuilXVUGuqMwCVib7HaWpx1pdR7rOjiHW17q9XVEaUNQ3ox5DchgsDw9cDkW8881sj//rf319AmPJ6IFRVRGmqUKQHcyikEuDsj9rwSPW0pTyLR4SUD8fpyc8VMbN8etn9pqfzHZos8Ta+x9msU0C4RaK1/BCYC44GpwMFa62VRKU0swOfb/ZDM7RZDUVkpicVNmyA7WyxrfT1s3hyMCJqaYMMG0gvFClSuEmN/++3w9NPwxBMEHwC/P2ry0O5EBC0MUHk5zlrxjJxrfhLSCxix8HWL6+ogMa5RIoKbbpJkcbJq/q3DqKwUr/G778RrjEKf212kIbx4vQrmzpX7Gx66NTbCwoWweLHc86KiDnWBqakJDiZavhz5z4IF8PXXcrxt2yKSf1dKQ7sQgd8Py5eTkGxFa0WjR7dOjE1N8OOPovmH1Ue4obXZwNukg8xgsfD4E9IOdkFVFXz//e6NmKuu3rWcjY2waFGg8lsiIhFUFstvTVa5tt15cKurobKSzWsbye3XiNomNz7iWAKtRQ429GOHQ9pNKIqLozYSrSO9hn4JXAYcCRyBTB73y6iUJhZQUCCxe0cfuIICmD1bZKCFC4Xm+/YNPtwZGbBuHdVVmlS7W1z/ggKSPOXYrH4qt7tY830l33wjhvj226FoVZVY1YSEqMlDuxMRNDeOFStg4UKcdvGKnP1S5cH89ltYvRpHvB93bVOzoXa5IEnXBevmxRdJypKD1VU2BU9SXd12fW/dKiyamQkrV8LSpZHJYPPmPU4+7CIN6Uaa6jxwyy3w3nu7RiNVVaJpNzRIA/35Z6mH7dvbdCSaowDjc0GBlDkrS4zUsmWwdm2L/4Qv8RgJnUkEu0iCW7ZAdTXOZJHJGnzxrecJ1q4NRjiFLXvauOu8OOKDdRMXB02NOtinOikJj8u3i/2jqEhIoLR09+ZlWb1anj0j9+DzSf02NMixwpysXXIEPh+OKpHB3I0WkTd35/w7d8JLL7Hlpwpy+zaIF9DQEJkIKivlOdi4EU45RZ6pioqWz/mWLVHLG3REGjoq5DUBmA7sm+MAmprEm6+tFU+vrTDMYPDVq8VA9ekjr8zMlnMFW61oh5Pqak1K7XaZtS0zE5WcRHqKjwpPAs885ScuDj77TNrPLXenBtePLC1tn5R8PnmIdiP7uNsRQXm5PIjZ2TgTLcHtmZnixRQXY1eNeLbugLlz8RftkGRxU5UQJcDXX5PUJI2vbs12mDNHfvv+e3n/4gtYtaplQelFjFEAACAASURBVN1uqYPERHEhs7ODjSQU9fXy3/buWzj8fqiooKGsDmdTtXizK1di0168RQGLtHq11G3ofdixQyogIUFIqm9fKePy5fDNN3KcDRvEGITcF4MIjj4aVizzyT7GM5OQINe3dWsLI7WLRNfYKOcvLBTyKyzE6Xe1uGd7gxYOgM8nxikjg6w08fAf+WgYurBo1z+WlEjZMzJE+1y3LnjtXi/u4goceJq9dJvy4fUpWdF9wQJwOHB7oGRnQH5pahJi+eknOWZaWgQ9pY2LqKyUZ9Nw0FatEskqI0Pu1dq1LQztLjmCqirilBeFH/fqTfKfwg52I/X7pS6+/54tDGaI3iT3uLKSwYNllxZEUFAg9//xx6Xc8+ZJ3Rk3tK4uql1sOyIN3RjyuhaJCpLa+1+PxM6dcgMzM+WpWLgwcssy8gDr1okBsFp33SdkNYv6uFR8fgupfR0tXI70ZB9FlQm8/GEG55/rY/x4uPXmJt74Opuv7/kuqEeG9qaoq5MHbPVqMXqGAZ07VxpTJDKIIFnsEhF4PCQm6Ba/NXuGcT7xxANJjuaIIPCOzQapqdgdCo81AaxWGhaKepjUWC7G8dxzwecjaf5nco6dLnEJ+/YNkmhqqhBxqL5cViYNKJRcExNlv1AUFgazjz/+2H5uxe+XlhiQZNwun1xPXR3s3Emc1Ye3rFLu7erVcs+NhLHfL4Y4fNi0cT1GP9zNm6Uss2fL81JXx/JlmqQkOPN0HwWbrdRZU1vOwaFUi9xSi/vgIJgvWbJEWGX9elixAueP82XfraVt5zN8Prme4uJWCbMF8VRWSl3abFx0cgWXn1jM9OcHcdn04dSXhkRfHo9422lpcg02m9TTtm1SdytX4nb5cTi07OfzYfN5hAgefhjuvx+0xt1opaxc4SvYIvW2ebPUqc0mhrKsrGPRemWllMNul/b8889Slqws+T0pSZyJEIdiF2lo507UjmIcuHEvWSnHqqnpmKNRWws//URtjZ9KMsgt/7GZSOx2yMkJIQLDyK9aJbKVUnJ/Q/MEJSVRHX23JyOLXcDQzi5It0Nr8XwMjS4tTSp+2bJdZYiiImHw7OyWjdhAdTVcfjn89rfg9VLjkn1Sk1qGdRmpXj75LpXKunimXiTSw7SplQxN2MnvPpyEd/5CeWANXXzLFjH4oQ05IYGm9D787e1D+WGZo7mRAdIQjfDY7eapp8RZhbCIoLwcZs8mafUi+a1CGlqzQSjfLn9wOkFrnNvWB7eHwGH34/ZYwOGgLjEbgMTC9fJAX3stjBtH0pfvA1Bcn7rrcltWq9T7ypXBa9i8uTlU0Rqefz+TN+YNkoZjGDyvl/kfVnLhv49k8v8dweRb9+cvV5ejva2E0bW1QvIrV4rR7duXBm8cTqeSxpqaiq2qnCZtk/tYWwvFxTzyiDin1NZK+SI4AO9+lcYTM3PQCYniFfftK+/bt8PcuayYW8mo3FpGJ2wEYNWOjF3LZ0zzGbAUzffB7pcy19RAv35i1DIyICsL58BMABp2VIs3OX9+s8b82GMweXLgdZabydekMflCxeSTq/jvbQW76N4tIoJt25pDEfurz/PKnFz+deVq3pqTw3Enx4mD7vWKoTUMr4H0dIl41q2DwkLcyoHDoaT8mzdj87jQWuH3BUh56VLcTRb8fkX5DxvFMcjKAouFrxcl8+Br2UIcIdHSZ5/BP/8Z4R4XFTWXu6TGwZQnxjH5wWOYfOv+/HJaf8qqrHLvjahAa9xujcNXJ+RQVyfHmDsXB25Ka+KDkl11tdz/wkJxviLJRWVlEg3EDQcgd+tcqZ8AkbXoQrp1qxDdk0+KTTn3XJE/lQrKQ1u2SHmjhI7kCGYppfIDrw+BtcB7UStRd6GiQhpf6IOcliZGMlS0bGwMykEuF/zlL/Dss0G2bmyEP/9ZDNiSJfDss1TXicFITfJJwvPZZ2HFCtKTJTQeMaie4wcXAOCsL+fehHtZw4F898pGeZirqsRTWLmyueGTmto8Z/JXP6Twfy/mcNyfxvDa23HywHo84o1u2iRl++knpk/X/P3vUszmiEDXSWSRkkJisjwOdT+ug2XLaKj2EB+vsaxfK+f94Qf41a846bM/cxmvkfarc+Df/2724O1xGk+TeO6uBjlW0prFMGaMPOCTJ5NdtoKDs8uY9vgAnns/c9f74HDIfdi2TQxubS1UVeHZVMRVd+ZyzT1DmPb4APG+jfxJaSlPvp/DrLlprNnsYPHGNO5/pR8r3lzRMqIzuufNnSv1k53d3D20wWMJRjiNjcSV78CbkgGTJsm2ggL+fG8qL7+MPBOhJFBVBU1N+P1w4/2DuOG+wVx821Dq3YEoxmqF9HR0n74s35LMqP1cjOovxmz5wnrpIRDelzQjQ+5jaSkNlWKZnTU7xTgZXm0IbDbo36eRZYWZQj5aw6JFuLaW8+c/CzesWe2X145U1hSnMmdVJrc8NpjG2fOFqAIOTzMRWAISVFKSPM/PPYfyNnFr9st8cO9K1m6wctRRmoVvbhLjbHR7NGC1iqO0fj1kZeH2WHDYAxH32rXE1Usv9KacXCHgmTPxNMlzU6KC9wbgodf6cst/BnHmXWOpWrMDrWU8xumnw1//GpZWaWoKyonAqx9n8Oonmaze7GDpj35e+TKHeS9tFMKtroZVq9Czv8HjUTgqd8hzPm+eHOeLLzgxZTEvcRV//WcyfrtTjPK8eeJ0eTxCBuvWBSVaQzL+/nu2HHAaALneDbKf1Qrr1pGbq4UIPB4hgmXLJMK79lo45hi5CVu2yHVUV8t3o99tFNCRxesfCPnsBbZorTso1MUO/H5YvsDFoYdbIne/2LQpmLQKoKbOQkpqqoRsmZnyYG7aFBx1dcMNuFZswvH1N1gXLIB77hGN78cfcU//F5Yli4h/8UWqM88ARpG66Ev44Pdy8GefJd3+DnABUy8oR1WUyzGXL+essheJ537ylw7muPLy4GLC2dlSpqSWXdjy56SS4PBx1EH1XHH/oSzftIF7r5uPFZ8YO4Dyctz1fr77zkJpqQpGBOt/gnQn2O0kpYlxc9lSoXQ9DRuTccQNEs/k9dfh0UehXz/GTr+I18ZmwAvnwsyZ8MEHMGYM9prXcTukbusa5FiJFVvhhtOlkRx9NLbsLOYOuISLh8zk2nuGsHyVjRsvLUPFWVFAbk4jVsMIDhgASrHj2ts5v/hxvieLQwaUsawwixprOilbt8J++8GGDaxYOpCT/F/w0ROwQ+WQM+lQ8mcnMTp7HhxxhJDAqlVSx1lZYLW2qMsWRPD559i8x9CQMRz2k5nIfOs20uS1SBBSWCik/Nln0ngLC6F/f5Zc/TTFZUcyaXw173yVzoZtDj54cAOD+olMtbPcRnl1HKNHNrLfCBtOu48Vb6+C8hfhxRfh0EPh0kvhpJPEYCQmwuLFNBQkA8fiqIhMAgbOOraaNz7PwNOosDudoBRfvLANjyeTN96AEzKWC2kHDPasOank3TyMOZsHc7LlZyG4gw/G7Raz4HBXgVMJQdx7rzyHmZkwZw5nPzqZBRnfk3fPWCb+ej+enBbHxCNrwdMoRHvMMZCYgM3aj8HZHpRF4W7w47Aj15aUhK1BIjrviadi91Tgz/+QRoMIKuNoXqvK5aJoRQX9nX5m/5TG0VfYOXy8j7f+Z+WMM+DjjyE/X/wvIJjIf/NNuPBC8ueM4JDh9fx8w3Ns+OPjDGcdtZ99B78fLA5VURGNdlEC7GlOkSlBopzCQl7/+0JufM7NP1fmseIfFbz2h0Uk5yQJ4QIkJNC4dhPbFpYJeVitUFQPZSn8dMipAOQmV4oMefzxsG0buem5vLctBX9hMRat4ZlnYNAgOOusoJe2bBkMHgxbt+L1KTb99mGyp55LyoEHtvoM7Ck6kiP4NuQ1vyeSAMD06XDURCclM+eJVxiqIdfUCPPabPDWW1BaysqNDrJOPpR35/cT47F9u9ygggJh5htuwL2qgJGpxUw7NnDM88+Hzz9H33AjJ878HRdWPgNDhlD99BsApHwwQxr5J5/A9OnkpNbjoIFfHR7ojVtUBPPnk0wdJ4woJF+fBR9+KHJVaipfL0om46TD+O7noDatNcyam8Zpx9Tw+RPrmXp+Kf9+ZxivfDMoOHwZIDOTBrdCa8XHL+ygbpMknhLt3mbPKdEphrCuQSSaEncKSU6fEMHzz8MvfgHvvisPa9++MG0a/O9/cMEFsH07juICPD+vgTvvpGq7PMzJcR448UTxGGtq4IILSP/xKz5OvJA/Jv6XR2cOZPiFhzHs3NHsf+5o/nRXitwHq1VId8UKzit+gp8tR/C/pKu4t/BKAFZsSpRyrVtHU2EJq2sGMMr3Mzz2GP2yvIw92MWsH7KF3BculOjMbpdGbrXyzeIkMk46jHlL5dob3AqHzyXaz2uvEeeMw+tMFtIfNgzPGslJ1JQ3SYR4220SpY0cKQNAgFn3/IxF+Xl1+kY+fHgDG7fbOf33w5uVxRUbhSRH7e/GYoGDM4pZUd5Peib98Y8SlU6bJgQDcl/69qUEMThJOcktpUi/X65tzRrw+Tj7uGpqXVa+/TGQwnM4mPVDX1KTvBw7okQIK2Qwy0lja3DY/cz6LkOkph07YOlSGupEUnNUFIockZ8v9fKHP8DJJ0sEWV/PwYNr+eG+bzjmEBdX3z2EYeeOZtjFRzLs8T8y7PKjGXbuaIacPZrn87NgzRrcKzbgKCxovjZbmXTN9E48Cc47D09IequkIuCjLlsGl11GUVUCZza8y1f3/0RlnY23/mfl7rvhw9eqOWxYLbPeCdHti4uFHV5+mYoLpzLvpwTOPqgAbruNlP2ESGtK3dJZwW6HjAwa/KIEOOJDnKxPPwW7nfhTJvL071fxGDfw8XdpXPPsUS2TCRYLFz80lmG/HM+wqycy7MpjGfbXixjGRm7/+gQSHD76TRguUYTXC5mZDFbbaGyEksVbRQZavx6mTpVnPy0Nhg2TetYaiospm72cEWtn8dqSA4gGWiUCpVStUqomwqtWKVUTldJEEZdcAk1eCy99O1R0y2+/FR31iy9ErrHbxdjdfz9MnsyT/1dJk9fCI28GNN61ayXcs9mk0a5ZwzsX/4/C6mSe/WksruffFM/zl79k0Zjf8P2yJPLnZbLxD49S0yAhXepZx4mg2acPnHUW0x7tzwI1nsxv3hWDtXWrGKzsbPLOtbKeEax9Z3lzyP7om33x+RSPvdVXGsjtt7P0ppfZvjOePMtHxFeV8PhfpJ/x9opAdBMYqu7zyfUD5H9owVXiwmb1E58VnPciPk4TZ/PjcluoqrXywbfpnDmhBl57TeSaG2/cdejl4MHwpz/BzJnYDz8IT9YA+PRTlv3tLQAOHpcs0oLfL++nnQbJydiW/8TDY99g9rmPMGP808wY+g9Os3zBCx/nUFfjl8aQlsaSl5azgGP49007mPz5dYw6bwQAK74tF6O2eTPrP1pHE/GMHu4RA7B8OXnHVbFwRRI76pIkKsrOblH2R98K1OWr6fDYYzRUN+L8+B0Jzdevxza4P00+JfU3bBjutSLo1pZ7xPh6PPKs3HcfXH01vPYa+YmX8gs9j8zrL+SMn//JoxfNY2WBk2+WiGE2iGD0sAaoqmJ02Tcstx0OF18MV1wB77wDo0fLMUMS5jM+yiQl0ccvDgtJzm7eLIbjd7+T/554Iie9dR1Oq4f8V2uhoACfVzNrQR/OGFNK3PIfxaEwku6lpSR89A6nDNtM/pw0ecSysqCiAveazQA4murE+XnkETjySDjnHFliq6lJZI6sLDKHZ/D5E+t5984VzBj0N2aoXzFj2F3MYAozLvqQg/dr4LE3stDTbsOt7TiKC8TTBmzrZTK/pqEjYORI3CMPa768nTsRyezaa2nyWSihL/0pZEL1hyx9/kcWvrSav1+5HfXdfPJ+Uc78xXbKlhVJ5FlcLFHJqFF8knMVPm0lb9a1kJRE8gP/AKAmZaBEYYG2VRvI46UkBvJKXq/YhuOOg8RE1HETuCHhRW4a+gHvfp1OUWlQptlSHM8H36Zx2aRyZty5iRl3FjAj449SD3cW8NVd32E55miROZcsAZuN5Az5v6vWL+1r4EDpNgpSv4cfLvXk94PPh3vmxwA4DxxCNNAqEWitk7XWKRFeyVrrlNb+F6s46CCYcEQdz340AH9Glng6SonB6dNHdLhXX4WJE3GNOppXfx5NiqWWuT8ls2prknioJSVigJctg9tu45nVE0hJ9FHjsvLWylGS7Pn973lmZh8SHD6sVs1/fxpD9UXXAJB6/SUtPLqsYWkcemyyeP3x8eIRLl0KxxzD2ceJfppfPAZ+/JHtO+P4cF4qKQlNvPtFMiW/vhW++478pYNR+Dnjq5vhkkuwfT8Xq1XTUB8INydNgmnTmjtaWK2az5ZkUu5OJNHpF7vw7bfw/vvg9ZLo9FNXb+XVjzNo8FiYetJGCbFPPVW8lDbgSLHjTs+Bt99mcdrJZLOD/hcdK/pmSop4z3Fx8OWXEhXdfz/H//1Ypjx6FFP+l8cd15dQq5N48/6tcm927OCZlb8gweZhytmVEB/P4D+cRxK1LP9ihxwrPZ0VX0pf71G3ninG7P77yZsgGvyH81J3KWdRaRz536aSEt/Ae9+ks/PlT2nAiXP8EZJZff99bP37StrHZoMDD8TdKAa0ptInRqZfPzHaAWypy+Tnuv3JO9Ujz9SMGVz04iTSqeCZ3y6DU09l+YuL6ZtYR5+kBnj8cUZ5l7LTm0VpVZxxc+Af/xCSufde0JryKiv/+yqdKWeUS8Tm98N//ysS0saNEpnccw+cdhrOki2c6vuUWQuy0BddxA+3vUdpZRx5p9RLdOF0ijxx1VUirv/zn+St/D82F9lZsTHg4WZm4q6Q3lHOBCVyoNstQrxSIl+lpEgdWCygFHENtZz/+mSmFN/HlH8exJRXT2PKwT8x5bMr+P1ZBSzbmMTCwoF4+gwUR/qee6CsjLgtkjD3+qRuPacFe6WXPJcvhvr009n56FtoLPRPqoU5c+ifG8fYjA3SDjMzOfukBvx+xccvl4qTt2GD5I/OOYf8/W6iX2ItYw6og4cfxjEwC5tVUzvqGJH3fvhB7qtLpMwUe6ChLFggToCRI3I44IQTmFo8HZ9P8cIHwfzWc+9noRT884ZCppxZwZSRi5hS8QhTLnQzZeI2xo1DnhWj/gFHkkQ87q0lUo7LL5f7r7XYgZEjpd537oQtW3BvLm4uRjTQ4V5DSqm+SqnBxis6xYkurr+gjI1FTr76IVkauN0uD7PW8MADYoxvu403T3meGlKZYbmKeNXEMzOzJCro10+MYnY2Kw+czLylydx+TTEH7dfA0++KrlhVa+WNzzK4/PQKzp5QxQv5mZRmjAR27TUEQF6eyFILF4on43LBuHEMym7ksOF15FvOg5kzef4JNz6f4nXPZJp0HC+NfQpmzWLWoN9wzCH19H3nKfF6b7pJuru994kYjAMOgNmzcb/wOgAnj63B1WDl4+9SSUrwi7zxl79I45w8mSRLPXX1iqff7cOYg1wc+d1jkgC/7rpgmbUWTzGsq6o93o+n0QKDBrE46XjGHG1FHTNOrmnQIDHS8fGtDtM/5sqRjHas5+nP94PaWmpem8XrXMalp5SRGtDyLUkJjOpbyoriDAmnN21ixY5MrMrHAQcqiVpWrWLU2nfJzfEwa05IAtPrhVmzeP66Bfj8Fl5vnEwT8Twz+XM0FpyHjhBte+BA4mxaBjvtvz+MHYsbaYG11YE6O/XUFqT+4VwhnLypOdIZ4Msvcf7zH/xq1I/M5DxKxuWxwjWUUa6FIq29/z6jTpBnptkIAwwZIr3N5s6Fjz7i5Q8z8TRamHpBqdT7ww8LwZ94okQQF1wgxuqvf4W33+bsaQezlVyWHf8HZs1OxGb1M2l8rUSc69bJfrW1Ime98QZn/kIcjln/KWgugjte/DxH2XaJsC6/PDgc1mYTiXDevGDPrgceEOP7wAMiHdlscOed4HZz6TsXkEQtzwx/ALclEcehB4jkd+ON2LQ8P16f5CHc409sLkNJ3AB47jmYPp2iermH/Q/JkjEnjY3yLAW6lR5xQD39+zQya+lAucbvvwerlcZjT+TT71M56xQ3lhkvwciR0js30UdNzgFyjBdegAULqJn+EAAp9/wF7rgDZsyQiHP8eHlea2vh9NMZVr+Mkweu5tnXE/E9/ChNjzzJc28lcfohRQyuWi5S6X33CWlOnCidFYYOlfofP16cLperOR/l/vBLOc/ZZ8uFV1fLdRlOxpIl8MYbuJNFHmwhXXUiOtJrKE8ptR7YBHwLbAY+iUppoon33+eCV88jM9nDMzPD1j3+9luRh667DrKyeHpmHw7er4G8SxM5X7/DjFnp0gNk/XrR7S68kGc+6Ed8nJ8rT9jC1JM2smhVIj+ucQY96XN2MvXkAkor43j5Q/EekpwRbuKxxwrJfPCB9PKxWmW0UUkJeeNK+M4/jp2f/cRzH+dwqvUrzrwwgQkHV/Bs0Zlsq0llyepE8o6rEgPy4otwySU4fXW4/XHi3Qa8KvdLkqc4fXwNiU4f23fGk2hrFE06N1d6/zgcJFYX8fXHblYWOJl64FwxNmeeKfs0NYlkYfTIcLslSqqtBa2xx2ncjQpXg4XVmx2MOSSQh/H5JMlotYphbWUWR2VRTL24iiW+w1n8j1m89lEaLpKYeklLJXLUGAfLGY1+4UV47z2WWw5j+CC3zIF0+ukwahTq0UfIG72ZLxamyL1zu+GWW/DdeTf/LTqTk3NWcuZrlzPxiFqenC3Jt+ZkMWCzaplion9/OPxw3E7Jt9RUa7me005rUab8OamMGOxmRG7Ao0xOhlNO4bp/5NDkt/H80HtYaR3N6OMzYcQIGDGC0TdMBGDFhrDOC5deCocfjr7/AZ55LYnxh9QxephbItY33pDf77mnZQ4ogLNOcKGUJn//m8i3nc9x8QtIc3rEeN5xhxid554TOWv4cHIevIWxqWvIX9BHCEbr5ujH8fwTct+uuqrlSSZMEG95+XJpOx99JPsce2xwnyFD4MYbSS5ayxVZn/HmlnFU1FhxDMqSe7R+PbY06Q7prW+ErVtxW4KdNUoOORkOE6moqEwipv7jh4hhXbxYHAql4Ouvsdz6Z84eX8GnC9LwZOQIiR55JHMKBlLjspJ3XMvnLSXBK1LQFVeIob3hBmoKJXGdMmaE/P/HH4XU4uIkt+VySTSUlcXU7bezrSaNT9+qZtZrNeyoS+b6pVPleP/+t/T2ueYaIRqtpQ5zcsQBqKqCW2/FYZW20fDjarjwQnH1fT5pYwcdJB0l9t9f6nbuXBpOOEPuiT06Sxp2JCK4G1lPeJ3WeihwErKsZM+Cw4F90xqu8r/A+9+kUlwWSEZVV8NDD0nvk4svZsnqBBavSuT6C0pRv/ol1ztepsoVz9tfZEg0YLdTf/oFzPgog8kTy8hKcjPl13E47T6eebdP0JPus5VTT/YzJLueNZudJCf6pMeh1yvG1OijFxcnhnbOHNEkR40SI2u1kjemGD8Wfpf9LtsZxPV3D4BbbuH6S6vYuN3BHx+UJaENGQm7HW65BUdmIg0TTxfvVin4299wDxMPI71oBaceLvpzUllgUNZDD0kS+7XXSOqfwhbfIFKo5pJ3J8vDec018kCXl0vIevzx0iV04kQYO1aMXkkJDtx4GhVL1zrx+xVjDqoXmcMYJQ3SILRuNSq44iobCVY3T885kKe9V3PEkHI5TghGHeijnCx2frkcPvmEFc4xjBreGJzS8Y47IC6Os2ffTIPHwldz4iWvM38+n0x+gW2+AVz/RweMHMn1F5Sys1wMjdMRLFOc9uBVNmmgKSm4B0l/8Np6q5DiiBHN+9bUWZi9OJm8ibtOinfgUDcTj6jl/leycTVYGXVsmhD066/Tb1AcGaleVqy2irExYLHA9Ol8k3QW60rTub7+IXjlFdHqTzlF5m0KHWAXguxML0ePcvHcR/1Y6T2Asxvelh5fzzwjXvvf/96ym6fNxtmXJLGQcez4bz7ceSfuejE2jlVLJDoJHTjn9cpzZbXKiOD/+z+pi6sjrFV10UVwzz1MvWcQbo8FV4MVR7yWnFKfPtgOl2eyqboe+vfHXR4cz1BSFdTgiwNEkDNhmMgrc+bID1VVIqHNns3ZlTOoq7fyzUcuybWdeCL5c9Jw2P2cNDakbr1eku1N1FT7JZo691y4/XZq/nI3ACm/vxI+/1wmPLoxMLdmY6PkwlwueOopznn0ZPqlu3l63Es8PeY5BmXWc/q9E6QuZs2SJPPUqdLGk5OlzDk50nb+9jdYsADHGy8C4LYlCRGASEIjRkj0kJMjUcGWLRAXh/sXJ8k96UYiaNJalwMWpZRFaz0b6HkLzE+aBM89x3Xqv/j8Fl54uAb+9S8xwjt2wK23gs3GMzOzcNr9XHFGBaSlcdwVgzmA1TwzwyE3+IwzeGvhEKrrbEydtAXGjiV97HAuPrmC5z/IFE/61M0wYACWo47kusslwZea6BM5paJCtHaPRwyr1hIW+nzyAB9zjDxw/fpxxJGK/lke3t15LDlZjZx1ohzrghOryEz1MnN2OvsPdHPg0JYjHZ2JFty+kD7HDgcNN/1VPr7xImd/Nw2AxMYqqYOBA2U/q5XEfuKlXXGui6QH7xLjM2CAlL1fP/H0jO63Fot4O0ceCRMmYE+x4/HA4qVCskce6JJoYXCIkmi3i0xUVibGr7KyuR8+QGqSn0tPKeMlrmQZhzL1sjoUWvYPjAkYtb+8r7AdRr3Hwsb6HEblBuSPmhoh9RkzmDiskGRqmHXPz9Lr5a67eGbnOfTLbGo22uedUEVWmpzbGdLIbHhlQBlAYiLugZIfqfElok89LWiIGxv5/DNNk9dC3qGRp1Geen4plTW2QNmD90opGDXUxfJNSZJI37kz6CAMGMAzox8j3e5ih+bo3gAAIABJREFUctGjwYTtnXdGHsQYgrMnVLN1hyTGzz5qp5DAK68Ek71hyDteDOVHE++DDz+k4T0J+O0jhogXa8BYSayxUcrywQfiSE2fHrmPu8UCkyZx2BgbYw+WZ9dhD3QEmDWLuJMlIvL6FBxwAO7AkI+MVC87K4LHKyqNx2LR9O1ngXHjhAi0FkKtq4MJEzhxznQS4puY9YEflEIffwKz5qRwythqEhwhxrO8nJSsOGqbHHKMv/8dzjmHGrfUV0qiT65lzBi5Jx6PPFfDh8v+ubnEjT+KX59bycffpfLFD6lcM7kK62kni1yYkxN8NlwuaTsgkZjVKvV5/fU4Fsi0K+4xxwZnMrDbg20lI0OcQoBJk3A70oL1FwV0hAiqlFJJwFzgNaXUI8jo4p6H0aMZ/tTNnBQ/lyc+259pM8cybeCrTDtrOdO+y2PaYwN4/dMMLj2tgrRk0T/V5Zcx1f4yCzb14/ee+5jmv5d/vZTNgYPqmPDr4cL4FgvX/yUFn99CSkITl5xRI+GdxcKv/5yFzaZJdbhFOz32WAn5jj1WZIeSEvEwjZt+zDFi8HJyUPvvJw0ZuObcMuICdsker7kqT7z6vPHluziHjng/DZ6WG90pAY3xN7/mzN/kovCTdMAAOOqoFvsZ8tXUi6vE4x83Tn4wtM7WkJyMY2AWbl8ci9cm0z/TTU6WNzhlRyiGDpUG0q+fGO2BA4MyU1UV119Wiw8byU4vl55WIcYmI0MaWEkJo/tJ19cVR/6KVYdehtaK0f3LpV7j44VUsrKIf+5JTs9Zysz605h23Hf8ed01fDw/lavPaVmXv84rb643I1kXlxiP1xdoHnZ7MxH4sOE+PpBArKqCujry1x9IRobmmOMdwWlKQnD+iUGyOXi/llOWjB5Yxc+bkpn2zhimfTKRaY8PZNoDWdz66ABmfpPBlRfU4Xzvdeli+uCDu47GNqYnKCuTnl1NTeSNkXmADs6tY/87Lpd669dPIolQeL1QXMzoIbXk5nh4pHAy0ybM59MdhxFHI9Zbbmo5cK6iQu6Vzye9aUCixZDoqDVcf4HcM4c3YDpstubxYt70PpCWhie9HwCDsxuD3UeR5H6/zCasbpc8k6Wl8PbbQkSXXQb33otzQAanWr7if2tGMa3vC9z4/GFsLnaQd/i24ISB5eUwYADJWXZqvIktRlQ3J4vD83i1tfK8Ohxy7YHI7drzytBaOl9cfU4rq4mFPvs2m2j/LhdcfTWOU6T+DE+fGrEZXmw89RQ0OZKFjM48E665Ria9o6Wz0pnoyICy2UAq8AfgisDnu6JSmq7AoEHcckcCF96VyX/0zbBVQcjMrs54H78/dQ2U10vviORkfnm5j/+8sJln1VT4JA6L0jx5dwUqPZhrGDvBzpmnNDImp5Ck8Yc0e0jZ/RS/+62mqTZOjKrRsOLjxfjb7ZI8u+YameVy5EhpcGlpYLFw5aQf+Wp5X647r+XD9tu8Qt77Mpkpp5eJATXmqHE4cMRreXC0lgfM68XtkfDecfB+9B3Xh8s3VzIyN6wrKDD+kDoSnT4OGR5isAyvyFhEoRXINNSKxVv7MObAKjGKCQm7rmCfkCBLdIVixAgxZEuWMGZoOWdPqOLwA+pJTvTDTo/8npIC1dX0Xb6cPmmNLO97EmmHHw0/w6jBNZAd6GO9dq3os3Y7v7q1Dx/fls5/5ksQ2yfdy3Xnt5y86zeTS/ng21QO7lMCpZXQvz+27MwWQ03cw0Y1f67J2g+nq1qMwxFHsPgPTiZMANsRh8CGQFI2Pb25u6o9XnPrr3by9aJkuR4DLhenHevkpdmK/zyigEQgQQyIUqQm+fjthaViTC65ZNcK93jkdeSRQtQlJeBycfDhaZx8rJu8I4qFQJ9/XjzS0Pvg8wl55Oaitm3j2nPLuPv5HNZtHQc2zdE526U7dHMFuOWZPfhgieLOOEPu4xlnBPfRgbUF6utl35Al+S4+pYLHX0vnsAPdzSsW2axi1LxZQgDu9BwABvfzsHRdAq4GC4m6jqIiTf+0BolEjjhCIo0HHhDDeu21Uo7p07ny2qf5glf5T9nl8IGV/plu8v6wH1R5RTZMToaDDiIlRbFliy3oNMTFNRNBizyeIWEaA8cGDWoezT6kfyNXnV1OfJxmQN8I81p5vWIDQqeFGDBA1IfkZBzXXwlfgDs1GzzF8iz16cP8uaLGjRxp5cRBg2SUXFIS7uWBvE2f6Ewz0REisAGfAxXAW8BbAamoXSilJgGPAFbgOa31v8J+vx74HbL0ZR1wndZ61S4H6mRMmgS1k1bs+kNNjdyQQw4XryMwE2nGlXlsXjdFEmKHHioNLjQxhtjhDz+PB++gFkPjgUAjb2Uy+UGDpBvg+PFyzPp6abwBz2/c6emsP2BOS6/a7WZoYg0bfh4MfQ6FhhHSqLduhZISnNahuF1KrqGfDIhzV4nk4IiXxvfK3ZtblqOxEeLj+dvVEVafqqkR0mpFlzZgt0u7WbPWwmWXpEovpvT0dv8HyD6JiXDggbBoEfkPS9dC6uqCU2qAEORBBzFqcA0rNjpJT5Gpjfc/2BHUYteulYJYLJxxbA21c5e2ft6mJobYy1nz1Hb57/7HyjgHR8s5vtx9g/JWbb2VbJ9LPDank6qqwGBUpURCSEmRro319XL9WnPLuRu45bQGqHEEDWRdHWdfO4q6W0PrR8HWwMhlwwBFgs8nBnns2OBI2ICsoIAv5gLbnbCiRpyLUBgSz8EHSzTa2MjfLlgT+d6DGMTqajlXXJx4xps3S483A9XV8gxlZIh8aEyvHcgvJDSUs2SmTX6btxUSErAp8b6bnFIfRs+swel1QDql66tIPNBJUX0aQ0ZaxRlYvVqciKVL4eabg7MBHH4451zxLXVvZ0qkYLNJ29pvJHCEnNduh7g4kpOhpkZJBBlwGmpcVpISfFj9TWANyFIul9wDo89maqq86ushIYHn74gsBQLy3Pbv3/LZNybk0xpnQK5yNyqpu9GjwWJpDlLq6oAD+omtSUqioUbIxjGw9ZHle4N2iUBrfSdwp1LqEOBi4Ful1Hat9clt/U8pZQWeAE4BtgOLlFL5YYb+da3104H984CHgEl7dil7Ca9XvKuxY4PJzf79ZQZEhwP+8x/Zr7ExspdrwNYRbg2BwyENuLBQGlF9fUsJpn9/SfKBNH6j2+a4cUEP3emUh37QIKirw5FqoboGIZbkZKirw/25TMbijKQx1tTIMf1+KUPoNfgCI4vbMkohl2LgyLFW8d52dxEZYyI1Y51LlysomxnIyGD0ATt4Pj+dlEQfBw2uwzo0YKiNHERRUeQIxuNp7uXUvP+IEUJaIVOPNK+na/zNGuzRUlOtYUBcc6+dXabZyc4WLd6YHNBikW0HHigj1HfulPPn5ETs+cPAgfI8NK/1+f/tnXt4VNXd7z+/ZEImCeEeEOQWBOU+wQTEC/ZVimLbF6uCVKpHbcXWS2tPW1/x0VapT1s9r49aH61H2spR63lFsReet3gH9bRVISreQOVqDSggYEKQQC6/88faO7Mzmcltsmcms9fnefJkZs+ePWuvvff6rt9lrRWHfftManBJSfzP3XJs3Bhd9QrM7+7ZY8Rh9GizbdKk6PxLsQMGwbhWhg2LTm8xeHD0ngRz3xw9as7ZDSz362cGbHpdWccfb26SceNg61byjhh3R0OT+e+GR0YMMskBe0aUM/qkYnbtEU45HXM9m5pMYPrNN02CA5hOUO/e8MMfmlTXkhJzjsccE/1tTz336ePMVzh0qBmV3dRE9YEm+hbUm/utoSH6LE6c2LIujjvOZC01NkYthtiZbkVMfcQ+M3l5pmwHDhDOdyYJ/BLjJXDK6tZBXR1GdNwJ8Q46QlDQgU5VF+hMq7UH+AzYB7TfKsAMYIuqbgMQkceBc4FmIVBVb15gEc66yL4RCpmbPd7DtW+f6Wl4MyR69TIP5WefRZ/0gwdNsLcjvdyO4k5F6N5Y3gasqMjcPJ99Zh7SwYPNA+wxu1vQuzcFA2H3QaA4uu1wiWkoWwWb6urMjX/aaaaXuGmTEboiZwqHmhojVLG+6Th425DyclpPH90RxAQO+ec/zfXq06d1YynC5JP7cOiJXF55qzffOv1TGOhpEEeMiL/+7dGj5nwmTIgOsCooiBt8bV5P16FOoyd3cM9hOK0UcnOpqzNV2EpzwmGT/ujmkLv1N2SI6QHu2JF4gF5Ojmmc//EP893Y8u3fb47TVswGTMNTWmosW9ei/Pxzc/8cd1zLskYiZnyEMwVHM198YY4z3jO1QXGxOR9XYA4cMMf0PjvFxeb83emUI5FoT6G0FHbtItTkjCNw6tkd9Djy9FL4A+w+3IcjR02Rhw3DPLf5+SaudfLJZuf6elM/1dWmTkpKzLZwOOEzUlxsHuOmvHxyRoyALVuoOTKGPoPyTOxjxw4jdKFQ63tv0CAT12poMPUUCkUzg9wl+g4dMiLet/VgRiZMgFdfJXzUdP3rao6aa+FOfuh4ZA8fxlz7/HwzT1jhlOZL5QftCoGIXA1cCJQATwKLO+i+ORbwLq9VBZwU5/jXYNZF7gWcGfu5s8+VwJUAI70ZKJ3luOOiWSpuw65ORsoxx0Qj/F6GD2+5PFxjY9u9sK5QVGR6J65PPXae+8mTTQ+ud+8ONazhcOtlFOqKTEMQrq+l+bI3NpoHaObMqBU0YIBxS7gZTTk50ayiDvwumHbYneuuS/TrZ67H9u1m8FKcc558kqmjo/U5xmDwCpUztTSffx5d9MV1pVRUdMi6ycuLdvpEoK4h+qjUHMo114vokIjYiTeB6Mj1WPr2NQ1jW/TpY4Ri82Zzv7liUFtrKtpxJbTLsceaY7jxor59TaMeW6eDB5tG6sMPTV26M+/27m0su5i5dRg2LOp3b2qKWhdejjnGPHM1NU5L7hAKwdSphDabWI0rBG5veNQ4cy337DH9H3C+LmLqfdeuaL1WV5t6cueycrv7paUJnxVXHw4dguIxY4xr6IEB9OknkJdrLJahQ81DFDvVeG6uqadEFBQkuBk8n0+fTvj/vWrO+Yi0aHdaCIEb5N++nbpi0+akTQiAEcCPVLUNR2vXUdX7gftFZBFwM3BpnH2WAcsAKioqum415OebhmDdumhPp7bW9HiPPz7+jeMEjKmrMzdBOJzYXE8Gt+fm7am5hMOdugPC4dZrZ7hZB+FQgwmIgnkCJ09u2evp0yfa22psNA95B6e/dS2Ciu5ILj7+eNOzSyC6kyZFX085Oc71iERM0HbHDtP4ffGF+VIHRACinhQ35uetz4N5/Zt90+7U+G09+11m7NjoCmFuT/foURNP6uiUxIWFpqHZtct8p6ws/kJKYHq6Q4YYMdi1yzRCkUj83zrmGFO3Bw5Es2riccIJUfeil/79CU00ZpTrWWl2DZnhMezZYzxr0Ky75vrt2BE9TlOTKcvgwWa0c+/e5qK10RNxhaCmBoqPNVahqyHN9O7tz3MOJgZ1Ujm5OU0mLdRTdy2EAIwCFhdT93oeIh0yzLtER2IEN3bx2DsxIuIy3NmWiMeBB7r4Wx3HNS3dlYBOOaXtp1jEPCDvvGMeoDFjutct5NK3rzl2BxuqtigoiCME7hzzZ5wMvQ8bAayvj28FueTmJm404uAKQXl5Jwscj969TbymjV6d61GbPDPOAxsKGf9uSYkJLI4ZE50moQO4bV88IajJj14jNzOxnYSqriFiGtJevYzLTiRqvXWGUaNM1/rEE+NPwe6lqMjsN3Zs88DGuPTpE12FrK16dVcri4O3jiFax/37N49RZJezImazQeFOnOdmKLnLTrrnuX17u424m8jjXcgt1mjxnYEDCRcodQUt255WQuBMvuiunuZH0wOdixF0lvXAOBEpxQjAt4BF3h1EZJyqbnbefh3YTCoIh6OpnB0xr0tKzBVoo4faLUyd2i1XOq5ryBWCwpyWI327EbeN6RYhgHbrYvJk0xAfO7INsSopMSOhc3M7Vbdu21Vf31pYDzZFA8euEPhiEUC0I5Kfbxq/eMHl9ujXz7jYOtPDTRSDcsnNNZ2IvLwu+yu8VhdEYwRuKCyuEOTlGXffYaczM21a9IBjxhg37qhRbV5rr0Xg0soiSAEFBUJdQ0trq5UQeLb75RYCH4VAVRtE5FrgWUz66EOq+r6I/AKoVNVVwLUi8lWgHjhAHLeQb3RmtZ+8PGOv7t7t63Jx3SX3bVkE7XUIk2HOHDPm6att5pN1H0uXmrTudqutCys7xTZSZuCnUl8PNQejnQdfXUNe2rLcOoIfbo7jj+9YRyoB8erYjb8OHmwet127zPsW6/EMG2amaA6FWqZVh8PG2m/nXBNZBKkWgngdtkRC0Go95W7GT4sAVV0NrI7Z9nPP6+v8/P1uZdSoaOAxwwmHTU/Wu6yuG/fqbHZrZygsNKndqaK8vButjxhc7fD6rwsKhHC4ZQPiq2so00nyZvJaXdCysRs82AxF2LXLxAda6E2/fiZWMnp0a5GPHcUeh1iLwI2jp0MIEnXY4m33Uwi6LudBo6goyVSY1OHeMN6bye8bKduI11sNh3EGI0X38901lMXEixG49+iQIVHXUCvffWGhCRB30akfaxHU1hoxyAQhSJdFYIUgC3HdP1YIuk48iyA/3zMYyeHAAbPd1m3niRcjcBMOBg82w1qqquK09yLGFOyi+sZaBO7/eGn/ftJZIfDTrWuFIAtxGyXvzWSFoHN0xiIIpFuoG0hUx2CEoKnJDIGI2/HvQtzHJdYicK9n6oPF1iKw+Ii1CJInkdsinkVg3UJdo70YAZj67+60TmfKoVYWQSa7hvzOGrJCkIUkihH4aVpmG4kaqXgWgRWCrtFWjMA7nKZ5MFk34U7Um26LIJOyhqwQZCHxXEN+9yiyjY5aBNY11HXaixG4+DHQq0+fnmURWCGwdBrrGkqejloE1jXUddqKEXgT9PwQgkyxCGyw2OIbNlicPIkaKdcicGextq6hrtNWjGDAgOjYgSBZBHYcgaXbsOMIkide+qhrETQ2GpFVta6hZGgrRpCTY2YH6dWra7NqtEc8i8DPSQPikUlZQ76OLLakB+saSp62LAIwjUhjo/mzFkHXyMkxgdt4QgAmTlBQ4M9g/j59zPx0YGayLiz0d9R9PDoTLO6xcw1Z0keiYLHNGuo4bVkEEF3UDawQJIN3AaDYBdLGjjWLhPlBrEWQ6sFkYO6nI0eia15AfCFQtRaBpQtYiyB52hpQBqYR8U6bbOkaoVD8GAHA8uVmUJkfxMYIUh0fgOi5HjnSuvPmuh5di6mpyQqBpZPYGEHytJU+CqbxcIOZ1iLoOnl5iV1DfvbSnaW8aWpKvxC45+1OFFlUZFZPcwUiFTMH22BxFmKzhpLHm9Hirs0eaxHYCeeSx+saSuU96jb8tbWZIQQQfV5dC9N937yWiM0asnSG2BssFT7GbMPrGnIXTIm1CAI9BXU34QpBU5MRXW+MwE+8gp4uIYh14aZTCKxrKAsRMQ+UeyO5QU0bLO443mCxVwi8DYi73VoEXceNEXjrOBV4BT3dFkFsg++my8YKhBUCS6fx5iin4kbKNrwWgbdH5m1A3HpNR8ZJtuDGCFLR6/WSCRZBIteQKwTWIrAkjTfIlOqHLBvwWgTe+issNEHigweNf7m4OPX559mE6xpK9T3qNvzV1VYIwApB1uIdrGKFoPMksgjcmStrakwjYt1CyeEKgXfh+lTgWgS7d5tMnZ4gBD02a0hE5orIhyKyRUSWxPn8xyKyUUTeEZEXRWSUn+UJEl7XkBWCzuNNH42tP3cwkp1nKHncGEG6LIKqKvM/XQPKIDMsAt+EQERygfuBc4CJwEUiMjFmt7eAClWdCqwE/pdf5Qka1iJIDm/6aGz9uYOR7DxDyZPuGMHOneZ/JmUNZZUQADOALaq6TVWPAo8D53p3UNW1quoOIn8NGO5jeQJFPIvAZg11nI5YBHYK6uRJd4zAtQgyIWsoUfpoKpI9/BSCY4FPPO+rnG2J+C7wdLwPRORKEakUkcq9e/d2YxGzF2+w2GYNdZ6OWgRWCJIjNkaQqnvUXa4ynRZBrGsodsqSVLp2M2JAmYhcDFQA/xnvc1VdpqoVqlpRUlKS2sL1UKxrKDlyc83/9mIE1jWUHLExglQFi8E0/plgEWSCa8jPrKGdwAjP++HOthaIyFeBm4CvqOoRH8sTKGywODlEEgcy+/QxbqGaGmsRJEu6YgRgBP3jj83rniAEPTVraD0wTkRKRaQX8C1glXcHEZkGPAjMU9U9PpYlcNhxBMmTyH9dXAyffWZeWyFIjnTFCMA0/u5KczZY7BOq2gBcCzwLbAKeUNX3ReQXIjLP2e0/gd7AkyKyQURWJTicpZMUFFjXULLk5SW2CNzpka1rKDnSFSOAliuSpXp1MjD3l0hrISguNoMWY59fP91mvg4oU9XVwOqYbT/3vP6qn78fZOIFi23WUOdoyyJwsRZBcqQ7RgDmuvbqlbrfdRFpGctzVyETadmRO3zYlC/HR/9NRgSLLd2PDRYnTyL/tdeNYIUgOdIdI4D0zhUV22FzO2uxFr3f9WKFIEtxg8XuFNRghaCzJOqtei0C6xpKjnTHCLz/00GsELjnH9uRs0Jg6RLhsBEBb0OWDvO3J+NtpPLzo+vKWoug+4gVglS6hlxBzxQhqKtraRHE2+4XVgiyFO+oRbdH4TZklo7hDRZ7e2Q2RtB9eNcjyM1N7UyumWARxE4Xb11Dlm7Fm5qWih5FNhJrEbi4DUdOTnqyTbIJb4wg1a7LTLMIEgmB12XkF1YIshSvRZCKGykbac8i6NfPWlnJ4hXbVN+jmWARxGYNWYvA0q3EWgRWCDpPokbKbTisWyh50ikEPcUisEJg6TLe4etWCLpGexaBzRhKHm+MIKgWQSYIgV2hLEuJFyy2dA63t6rasv7c5SqtRZA83hhBKjOGoGdZBH7H+KwQZCnWNZQ8rhA0NLSsP3e5SisEyZMJMYJ0DiiLzRqy4wgs3UqsRWCzhjpPItcQwAknwIQJ6SlXNpFOIRg+3Fh3J5yQ2t/1EtvgxxtHkIpkD2sRZClei+Dw4fSavz2VUAgOHTL+68GDW372j3/4O/dLUAiFzAR+6chsGzjQrCnhrkaXDjIlRmBv5SzFBouTpy2LIBSyQtAduI1wbW3qYwTe308XrhCothYC7xQxVggsXcIGi5MnnW6LoOCOJK6tDWYdu0JQX28sI68QQOo6clYIshQbLE6etiwCS/cQdCEoKDACUFMTfe/9f+iQuQftXEOWLmFdQ8ljLQL/8bqGgljH7jkfOGD+xwqBu91aBJYu4d5I7hQTNmuo86RzHpyg4FoEX36ZnhhBurFCYPGVUMjM5mhjBF0nFIKjR239+Yl3ttEg1nGsEHjHEcTb7hdWCLKYcBgOHjQ+yCA+ZMkSCpmeKtj68wsrBOZ/VlsEIjJXRD4UkS0isiTO56eLyJsi0iAi8/0sSxApKDB50hDMhyxZ8vKMkIKtP7/wpm8GsY47KgQ9NlgsIrnA/cA5wETgIhGZGLPbv4DLgP/rVzmCTDhshSAZ3GAx2Przi6BbBIka/FRbBH6OLJ4BbFHVbQAi8jhwLrDR3UFVdzifNSXzQ/X19VRVVVHnDtGzALB8uYkTXH01DBgAmzalu0RRwuEww4cPJy/dI3raIOi91VTgFQIbLM5OITgW+MTzvgo4yY8fqqqqori4mNGjRyN2pZBmmhx5PXwYSkvNkPpMQFXZt28fVVVVlJaWprs4CQl6bzUVBL2OM0UIekSwWESuFJFKEancu3dvq8/r6uoYOHCgFYEYcnKiro1Mmg5BRBg4cGDGW3DWIvCfoNexe87795v/sULgbu/JQrATGOF5P9zZ1mlUdZmqVqhqRUlJSdx9rAi0RgQaG6OvM4mecL2C3ltNBUGv4yBYBOuBcSJSKiK9gG8Bq3z8PUsMOTlR91AmWQQ9haA3UqnAxgjM/9ikjtjtPTZrSFUbgGuBZ4FNwBOq+r6I/EJE5gGIyHQRqQIWAA+KyPt+lcdPvvjiC37729926bv33HMPX7rJ6t2Mt/G3QtB5gu62SAVBF9tMyRrytXlQ1dWqeryqHqeqv3S2/VxVVzmv16vqcFUtUtWBqjrJz/L4RaYKgdf70hFPTIMbULAAtpFKBUEXW69rSCRqFeXlmYy/bMgaSg8/+hFs2NC9xywrg3vuSfjxkiVL2Lp1K2VlZcyZM4fBgwfzxBNPcOTIEc477zyWLl3KoUOHuPDCC6mqqqKxsZGf/exn7N69m127dnHGGWcwaNAg1q5dG/f4V111FevXr+fw4cPMnz+fpUuXArB+/Xquu+46Dh06RH5+Pi+++CKFhYXccMMNPPPMMzQ05PDv/76YhQt/wMSJo3njjUoGDRpEZWUlP/3pT3nppZe49dZb2bp1K9u2bWPkyJH8+te/5pJLLuHQoUMA3HfffZxyyikA3HHHHfzxj38kJyeHc845h8WLF7NgwQLefPNNADZv3szChQub3/d0gt5IpYKgi617zjU1xgrwdtgKCqKzkloh6AHcfvvtvPfee2zYsIHnnnuOlStXsm7dOlSVefPm8corr7B3716GDRvG3/72NwCqq6vp27cvd911F2vXrmXQoEEJj//LX/6SAQMG0NjYyOzZs3nnnXcYP348CxcuZMWKFUyfPp2amhoKCgpYtmwZO3bsYMOGDezcGWLLlv3tln/jxo38/e9/p6CggC+//JLnn3+ecDjM5s2bueiii6isrOTpp5/mr3/9K6+//jqFhYXs37+fAQMG0LdvXzZs2EBZWRnLly/n8ssv77Z6TTdBb6RSQdBjBN5zjo0DFBSYWVnBCkHnaaPnngqee+45nnvuOaZNmwZAbW0tmzdvZtasWfzkJz/hhhtu4Bvf+AazZs3q8DGfeOIJli1bRkNDA59++ikbN25ERBg6dCjTp09qtvIyAAAPjUlEQVQHoI+zFuULL7zA97//fUKhEDk50LfvAKBt19C8efMocO7C+vp6rr32WjZs2EBubi4fffRR83Evv/xyCgsLARgwwBz3iiuuYPny5dx1112sWLGCdevWdaK2MhtrEfhP0MU2Jwd69TKTG8YTAjAuopDPLXX2CUGaUVVuvPFGvve977X67M0332T16tXcfPPNzJ49m5///OftHm/79u3ceeedrF+/nv79+3PZZZd1OP/e2/iHQiGanBSi2O8XFRU1v7777rsZMmQIb7/9Nk1NTYTbeTovuOACli5dyplnnkl5eTkDM2XUWjcQ9EYqFVixNefdlhCkYgp5m0vSDRQXF3PQmZ3s7LPP5qGHHqLWsel27tzJnj172LVrF4WFhVx88cVcf/31zX5073fjUVNTQ1FREX379mX37t08/fTTAJxwwgl8+umnrF+/HoCDBw/S0NDAnDlzePDBB2loaCAnB6qrjWto1KjRvPHGGwA89dRTCX+vurqaoUOHkpOTw6OPPkqjMxBhzpw5LF++vDmwvd8Z6RIOhzn77LO56qqrssotBLaRSgVWbKMNfez5x6aS+okVgm5g4MCBnHrqqUyePJnnn3+eRYsWcfLJJzNlyhTmz5/PwYMHeffdd5kxYwZlZWUsXbqUm2++GYArr7ySuXPncsYZZ8Q9diQSYdq0aYwfP55FixZx6qmnAtCrVy9WrFjBD37wAyKRCHPmzKGuro4rrriCkSNHMnXqVObMifDss2Y+v1tuuYXrrruOiooKcnNzE57L1VdfzcMPP0wkEuGDDz5othbmzp3LvHnzqKiooKysjDvvvLP5O9/+9rfJycnhrLPO6pb6zBSC7r9OBVYIouedyCJIRb2Iqvr/K91IRUWFVlZWtti2adMmJkyYkKYSZS67d8MnnxgXUXm5f79z5513Ul1dzW233dap72X6dXvqKZg/31gGR4+muzTZySefwMiR5nVtLXi8lIFh/Hj48EM4/XR4+eXo9jPPhLVrYexY2Lw5+d8RkTdUtSLeZzZGkMW4g8j8HEx23nnnsXXrVtasWePfj6QJ1zUU1J5qKvC634JqdWWCRWCFIIM46aSTOHLkSIttjz76KFOmTOnS8VwB8HNanz//+c/+HTzNuG4LKwT+4dZxKOR/ZkymYoXA0oLXX3+9W4/nCoCdXqJrWIvAf6zYJs4OsllDlm4hFa6hbMY2Uv7j1nFQ3UKQGRaBbSKymFS4hrIZaxH4j61jKwQWn7EWQXJYi8B/bB0nHi9gxxFYugUbI0gO20j5j3tvBrmOrUVg8RXrGkoO67bwHxEjuDZGYIWgx9PV9Qi+9rWv8YW7BJEPWNdQcliLIDXk5QW7jjMhayjr0kfTsBxBsxBcffXVLbY3NDQQaiM5evXq1d1VxLi4lkBXLYL2yp/tWIsgNYRCwa5jaxFkCd6FaaZPn86sWbOYN28eEydOBOCb3/wm5eXlTJo0iWXLljV/b/To0Xz++efs2LGDCRMmsHjxYiZNmsRZZ53F4cOHE/7e7373O6ZPn04kEuGCCy5onghu9+7dnHfeeUQiESKRCK+99k8A/vKXR5g6dSqRSIRLLrkEgMsuu4yVK1c2H7N3794AvPTSSx0u/zPPPMOJJ55IJBJh9uzZNDU1MW7cOPbu3QtAU1MTY8eObX7f07AWQWqwQmD+p1MIUNUe9VdeXq6xbNy4sdW2VLJ9+3adNGmSqqquXbtWCwsLddu2bc2f79u3T1VVv/zyS500aZJ+/vnnqqo6atQo3bt3r27fvl1zc3P1rbfeUlXVBQsW6KOPPprw99zvq6redNNNeu+996qq6oUXXqh33323qqo2NDTo/v1f6OOPv6elpeN07969Lcpy6aWX6pNPPtl8nKKiok6Vf8+ePTp8+PDm/dx9br311uYyPPvss3r++ecnPI90X7f2+Ne/VEF18eJ0lyS7KSlRbeM2yXruuMPcZytWtNy+cqXZ/qtfdc/vAJWaoF21FoEPzJgxg9LS0ub39957L5FIhJkzZ/LJJ5+wOc4MUqWlpZSVlQFQXl7Ojh07Eh7/vffeY9asWUyZMoXHHnuM999/H4A1a9Zw1VVXAZCbm0u/fn2prFzD17++oHkFNHdBmWTL/9prr3H66ac37+ce9zvf+Q6PPPIIAA899FCPnpraWgSpIS/PBoshi11DIjJXRD4UkS0isiTO5/kissL5/HURGe1neVKFd6GXl156iRdeeIFXX32Vt99+m2nTpsVdWCbf8yTk5ua2uZD8ZZddxn333ce7777LLbfcknChGjcjI96s096FapqamjjqmV6zK+V3GTFiBEOGDGHNmjWsW7eOc845J+G+mY6NEaSGUaNgzJh0lyJ9ZPU4AhHJBe4HzgEmAheJyMSY3b4LHFDVscDdwB1+lcdP2lpcprq6mv79+1NYWMgHH3zAa6+9lvTvHTx4kKFDh1JfX89jjz3WvH327Nk88MADADQ2NlJdXc2iRWeyevWT7Nu3D4guKDN6dHShmlWrVlFfX9+p8s+cOZNXXnmF7du3tzgumOUrL774YhYsWNDm2geZjrUIUsPLL8PSpekuRfrIhKwhPy2CGcAWVd2mqkeBx4FzY/Y5F3jYeb0SmC3S87LevQvTXH/99S0+mzt3Lg0NDUyYMIElS5Ywc+bMpH/vtttu46STTuLUU09l/Pjxzdt/85vfsHbtWqZMmUJ5eTkbN25kypRJ3HTTTXzlK18hEonw4x//GIDFixfz8ssvE4lEePXVV1tYAR0pf0lJCcuWLeP8888nEomwcOHC5u/MmzeP2traHu0WgqhFEGS3RSrIy4tvtQaFRK4hZ3nw1Nx/iYIHyf4B84Hfe95fAtwXs897wHDP+63AoDjHuhKoBCpHjhzZKgiS6UHHoLF+/Xo97bTT2t2vJ1y3X/1K9aOP0l0KSzazf7/qf/yH6tGjLbfX16vecIOqJzckKWgjWNwjksRVdRmwDMwKZWkujqUNbr/9dh544IEWLquezI03prsElmynf3+4I45TPBSC229PTRn8dA3tBEZ43g93tsXdR0RCQF9gn49l6lFcc801lJWVtfhbvnx5uovVJkuWLOHjjz/mtNNOS3dRLBZLB/HTIlgPjBORUkyD/y1gUcw+q4BLgVcxrqQ1jgnTaVSVHhheaJP7778/3UXwjS5eZovF4gO+WQSq2gBcCzwLbAKeUNX3ReQXIjLP2e0PwEAR2QL8GGiVYtoRwuEw+/bts41LD0FV2bdvH2GbjmOxZATS0xrPiooKraysbLGtvr6eqqqqNvPbLZlFOBxm+PDh5HlXL7dYLL4hIm+oakW8z3pEsLg98vLyWoyEtVgsFkvHsVNMWCwWS8CxQmCxWCwBxwqBxWKxBJweFywWkb3Ax138+iDg824sTk8hiOcdxHOGYJ53EM8ZOn/eo1S1JN4HPU4IkkFEKhNFzbOZIJ53EM8ZgnneQTxn6N7ztq4hi8ViCThWCCwWiyXgBE0IlrW/S1YSxPMO4jlDMM87iOcM3XjegYoRWCwWi6U1QbMILBaLxRKDFQKLxWIJOIERAhGZKyIfisgWEenSLKeZjoiMEJG1IrJRRN4Xkeuc7QNE5HkR2ez875/usnY3IpIrIm+JyH8770tF5HXneq8QkV7pLmN3IyL9RGSliHwgIptE5OSAXOv/6dzf74nIf4lIONuut4g8JCJ7ROQ9z7a411YM9zrn/o6InNjZ3wuEEIhILnA/cA4wEbhIRCamt1S+0AD8RFUnAjOBa5zzXAK8qKrjgBfp4nTfGc51mOnOXe4A7lbVscAB4LtpKZW//AZ4RlXHAxHM+Wf1tRaRY4EfAhWqOhnIxax1km3X+/8Ac2O2Jbq25wDjnL8rgQc6+2OBEAJgBrBFVbep6lHgceDcNJep21HVT1X1Tef1QUzDcCzmXB92dnsY+GZ6SugPIjIc+Drwe+e9AGcCK51dsvGc+wKnY9b0QFWPquoXZPm1dggBBc6qhoXAp2TZ9VbVV4D9MZsTXdtzgUecpYlfA/qJyNDO/F5QhOBY4BPP+ypnW9YiIqOBacDrwBBV/dT56DNgSJqK5Rf3AP8BNDnvBwJfOIsjQXZe71JgL7DccYn9XkSKyPJrrao7gTuBf2EEoBp4g+y/3pD42ibdvgVFCAKFiPQGngJ+pKo13s+cpUCzJmdYRL4B7FHVN9JdlhQTAk4EHlDVacAhYtxA2XatARy/+LkYIRwGFNHahZL1dPe1DYoQ7ARGeN4Pd7ZlHSKShxGBx1T1T87m3a6p6Pzfk67y+cCpwDwR2YFx+Z2J8Z33c1wHkJ3XuwqoUtXXnfcrMcKQzdca4KvAdlXdq6r1wJ8w90C2X29IfG2Tbt+CIgTrgXFOZkEvTHBpVZrL1O04vvE/AJtU9S7PR6uAS53XlwJ/TXXZ/EJVb1TV4ao6GnNd16jqt4G1wHxnt6w6ZwBV/Qz4REROcDbNBjaSxdfa4V/ATBEpdO5397yz+no7JLq2q4D/4WQPzQSqPS6kjqGqgfgDvgZ8BGwFbkp3eXw6x9Mw5uI7wAbn72sYn/mLwGbgBWBAusvq0/n/G/DfzusxwDpgC/AkkJ/u8vlwvmVApXO9/wL0D8K1BpYCHwDvAY8C+dl2vYH/wsRA6jHW33cTXVtAMFmRW4F3MRlVnfo9O8WExWKxBJyguIYsFovFkgArBBaLxRJwrBBYLBZLwLFCYLFYLAHHCoHFYrEEHCsEFksKEZF/c2dItVgyBSsEFovFEnCsEFgscRCRi0VknYhsEJEHnfUOakXkbmcu/BdFpMTZt0xEXnPmgv+zZ574sSLygoi8LSJvishxzuF7e9YReMwZIWuxpA0rBBZLDCIyAVgInKqqZUAj8G3MBGeVqjoJeBm4xfnKI8ANqjoVM7LT3f4YcL+qRoBTMCNFwcwK+yPM2hhjMHPlWCxpI9T+LhZL4JgNlAPrnc56AWaCryZghbPPH4E/OesC9FPVl53tDwNPikgxcKyq/hlAVesAnOOtU9Uq5/0GYDTwd/9Py2KJjxUCi6U1Ajysqje22Cjys5j9ujo/yxHP60bsc2hJM9Y1ZLG05kVgvogMhua1Ykdhnhd3hstFwN9VtRo4ICKznO2XAC+rWSGuSkS+6RwjX0QKU3oWFksHsT0RiyUGVd0oIjcDz4lIDmYGyGswi7/McD7bg4kjgJkS+H87Df024HJn+yXAgyLyC+cYC1J4GhZLh7Gzj1osHUREalW1d7rLYbF0N9Y1ZLFYLAHHWgQWi8UScKxFYLFYLAHHCoHFYrEEHCsEFovFEnCsEFgsFkvAsUJgsVgsAef/A4EKaPKbje+WAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_, ax = plt.subplots(1, 1)\n", "df = pd.DataFrame(eval_tracker['test_accuracy']).T.melt()\n", "sns.lineplot(x=\"variable\", y=\"value\", data=df, color='red', ax=ax)\n", "ax.plot(eval_tracker['train_accuracy'], color='blue')\n", "ax.set_xlabel('epoch')\n", "plt.legend(['test_accuracy', 'train_accuracy'])\n", "plt.title('Training Progress');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Training does not seem to be working here. Let's use a different optimizer and boost the learning rate." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [400/400 02:33<00:00]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " rval = inputs[0].__getitem__(inputs[1:])\n" ] } ], "source": [ "inference.fit(400, obj_optimizer=pm.adamax(learning_rate=0.1), callbacks=[eval_tracker]);" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_, ax = plt.subplots(1, 1)\n", "df = pd.DataFrame(np.asarray(eval_tracker['test_accuracy'])).T.melt()\n", "sns.lineplot(x=\"variable\", y=\"value\", data=df, color='red', ax=ax)\n", "ax.plot(eval_tracker['train_accuracy'], color='blue')\n", "ax.set_xlabel('epoch')\n", "plt.legend(['test_accuracy', 'train_accuracy'])\n", "plt.title('Training Progress');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is much better! \n", "\n", "So, `Tracker` allows us to monitor our approximation and choose good training schedule." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Minibatches\n", "When dealing with large datasets, using minibatch training can drastically speed up and improve approximation performance. Large datasets impose a hefty cost on the computation of gradients. \n", "\n", "There is a nice API in pymc3 to handle these cases, which is avaliable through the `pm.Minibatch` class. The minibatch is just a highly specialized Theano tensor:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "issubclass(pm.Minibatch, theano.tensor.TensorVariable)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To demonstrate, let's simulate a large quantity of data:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "# Raw values\n", "data = np.random.rand(40000, 100) \n", "# Scaled values\n", "data *= np.random.randint(1, 10, size=(100,))\n", "# Shifted values\n", "data += np.random.rand(100) * 10 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison, let's fit a model without minibatch processing:" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as model:\n", " mu = pm.Flat('mu', shape=(100,))\n", " sd = pm.HalfNormal('sd', shape=(100,))\n", " lik = pm.Normal('lik', mu, sd, observed=data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for fun, let's create a custom special purpose callback to halt slow optimization. Here we define a callback that causes a hard stop when approximation runs too slowly:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "def stop_after_10(approx, loss_history, i):\n", " if (i > 0) and (i % 10) == 0:\n", " raise StopIteration('I was slow, sorry')" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 0.09% [9/10000 00:01<25:51 Average Loss = 7.7692e+08]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "I was slow, sorry\n", "Interrupted at 9 [0%]: Average Loss = 5.6736e+08\n" ] } ], "source": [ "with model:\n", " advifit = pm.fit(callbacks=[stop_after_10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inference is too slow, taking several seconds per iteration; fitting the approximation would have taken hours!\n", "\n", "Now let's use minibatches. At every iteration, we will draw 500 random values:\n", "\n", "> Remember to set `total_size` in observed\n", "\n", "**total_size** is an important parameter that allows pymc3 to infer the right way of rescaling densities. If it is not set, you are likely to get completely wrong results. For more information please refer to the comprehensive documentation of `pm.Minibatch`." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/dependencies/pymc3/pymc3/data.py:307: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " self.shared = theano.shared(data[in_memory_slc])\n" ] } ], "source": [ "X = pm.Minibatch(data, batch_size=500)\n", "\n", "with pm.Model() as model:\n", " \n", " mu = pm.Flat('mu', shape=(100,))\n", " sd = pm.HalfNormal('sd', shape=(100,))\n", " likelihood = pm.Normal('likelihood', mu, sd, observed=X, total_size=data.shape)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:16<00:00 Average Loss = 1.546e+05]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 1.5452e+05\n" ] } ], "source": [ "with model:\n", " advifit = pm.fit()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(advifit.hist);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Minibatch inference is dramatically faster. Multidimensional minibatches may be needed for some corner cases where you do matrix factorization or model is very wide.\n", "\n", "Here is the docstring for `Minibatch` to illustrate how it can be customized." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Multidimensional minibatch that is pure TensorVariable\n", "\n", " Parameters\n", " ----------\n", " data: np.ndarray\n", " initial data\n", " batch_size: ``int`` or ``List[int|tuple(size, random_seed)]``\n", " batch size for inference, random seed is needed\n", " for child random generators\n", " dtype: ``str``\n", " cast data to specific type\n", " broadcastable: tuple[bool]\n", " change broadcastable pattern that defaults to ``(False, ) * ndim``\n", " name: ``str``\n", " name for tensor, defaults to \"Minibatch\"\n", " random_seed: ``int``\n", " random seed that is used by default\n", " update_shared_f: ``callable``\n", " returns :class:`ndarray` that will be carefully\n", " stored to underlying shared variable\n", " you can use it to change source of\n", " minibatches programmatically\n", " in_memory_size: ``int`` or ``List[int|slice|Ellipsis]``\n", " data size for storing in ``theano.shared``\n", "\n", " Attributes\n", " ----------\n", " shared: shared tensor\n", " Used for storing data\n", " minibatch: minibatch tensor\n", " Used for training\n", "\n", " Notes\n", " -----\n", " Below is a common use case of Minibatch with variational inference.\n", " Importantly, we need to make PyMC3 \"aware\" that a minibatch is being used in inference.\n", " Otherwise, we will get the wrong :math:`logp` for the model.\n", " the density of the model ``logp`` that is affected by Minibatch. See more in the examples below.\n", " To do so, we need to pass the ``total_size`` parameter to the observed node, which correctly scales\n", " the density of the model ``logp`` that is affected by Minibatch. See more in the examples below.\n", "\n", " Examples\n", " --------\n", " Consider we have `data` as follows:\n", "\n", " >>> data = np.random.rand(100, 100)\n", "\n", " if we want a 1d slice of size 10 we do\n", "\n", " >>> x = Minibatch(data, batch_size=10)\n", "\n", " Note that your data is cast to ``floatX`` if it is not integer type\n", " But you still can add the ``dtype`` kwarg for :class:`Minibatch`\n", " if you need more control.\n", "\n", " If we want 10 sampled rows and columns\n", " ``[(size, seed), (size, seed)]`` we can use\n", "\n", " >>> x = Minibatch(data, batch_size=[(10, 42), (10, 42)], dtype='int32')\n", " >>> assert str(x.dtype) == 'int32'\n", "\n", "\n", " Or, more simply, we can use the default random seed = 42\n", " ``[size, size]``\n", "\n", " >>> x = Minibatch(data, batch_size=[10, 10])\n", "\n", "\n", " In the above, `x` is a regular :class:`TensorVariable` that supports any math operations:\n", "\n", "\n", " >>> assert x.eval().shape == (10, 10)\n", "\n", "\n", " You can pass the Minibatch `x` to your desired model:\n", "\n", " >>> with pm.Model() as model:\n", " ... mu = pm.Flat('mu')\n", " ... sd = pm.HalfNormal('sd')\n", " ... lik = pm.Normal('lik', mu, sd, observed=x, total_size=(100, 100))\n", "\n", "\n", " Then you can perform regular Variational Inference out of the box\n", "\n", "\n", " >>> with model:\n", " ... approx = pm.fit()\n", "\n", "\n", " Important note: :class:``Minibatch`` has ``shared``, and ``minibatch`` attributes\n", " you can call later:\n", "\n", " >>> x.set_value(np.random.laplace(size=(100, 100)))\n", "\n", " and minibatches will be then from new storage\n", " it directly affects ``x.shared``.\n", " A less convenient convenient, but more explicit, way to achieve the same\n", " thing:\n", "\n", " >>> x.shared.set_value(pm.floatX(np.random.laplace(size=(100, 100))))\n", "\n", " The programmatic way to change storage is as follows\n", " I import ``partial`` for simplicity\n", " >>> from functools import partial\n", " >>> datagen = partial(np.random.laplace, size=(100, 100))\n", " >>> x = Minibatch(datagen(), batch_size=10, update_shared_f=datagen)\n", " >>> x.update_shared()\n", "\n", " To be more concrete about how we create a minibatch, here is a demo:\n", " 1. create a shared variable\n", "\n", " >>> shared = theano.shared(data)\n", "\n", " 2. take a random slice of size 10:\n", "\n", " >>> ridx = pm.tt_rng().uniform(size=(10,), low=0, high=data.shape[0]-1e-10).astype('int64')\n", "\n", " 3) take the resulting slice:\n", "\n", " >>> minibatch = shared[ridx]\n", "\n", " That's done. Now you can use this minibatch somewhere else.\n", " You can see that the implementation does not require a fixed shape\n", " for the shared variable. Feel free to use that if needed.\n", " *FIXME: What is \"that\" which we can use here? A fixed shape? Should this say\n", " \"but feel free to put a fixed shape on the shared variable, if appropriate?\"*\n", "\n", " Suppose you need to make some replacements in the graph, e.g. change the minibatch to testdata\n", "\n", " >>> node = x ** 2 # arbitrary expressions on minibatch `x`\n", " >>> testdata = pm.floatX(np.random.laplace(size=(1000, 10)))\n", "\n", " Then you should create a `dict` with replacements:\n", "\n", " >>> replacements = {x: testdata}\n", " >>> rnode = theano.clone(node, replacements)\n", " >>> assert (testdata ** 2 == rnode.eval()).all()\n", "\n", " *FIXME: In the following, what is the **reason** to replace the Minibatch variable with\n", " its shared variable? And in the following, the `rnode` is a **new** node, not a modification\n", " of a previously existing node, correct?*\n", " To replace a minibatch with its shared variable you should do\n", " the same things. The Minibatch variable is accessible through the `minibatch` attribute.\n", " For example\n", "\n", " >>> replacements = {x.minibatch: x.shared}\n", " >>> rnode = theano.clone(node, replacements)\n", "\n", " For more complex slices some more code is needed that can seem not so clear\n", "\n", " >>> moredata = np.random.rand(10, 20, 30, 40, 50)\n", "\n", " The default ``total_size`` that can be passed to ``PyMC3`` random node\n", " is then ``(10, 20, 30, 40, 50)`` but can be less verbose in some cases\n", "\n", " 1. Advanced indexing, ``total_size = (10, Ellipsis, 50)``\n", "\n", " >>> x = Minibatch(moredata, [2, Ellipsis, 10])\n", "\n", " We take the slice only for the first and last dimension\n", "\n", " >>> assert x.eval().shape == (2, 20, 30, 40, 10)\n", "\n", " 2. Skipping a particular dimension, ``total_size = (10, None, 30)``:\n", "\n", " >>> x = Minibatch(moredata, [2, None, 20])\n", " >>> assert x.eval().shape == (2, 20, 20, 40, 50)\n", "\n", " 3. Mixing both of these together, ``total_size = (10, None, 30, Ellipsis, 50)``:\n", "\n", " >>> x = Minibatch(moredata, [2, None, 20, Ellipsis, 10])\n", " >>> assert x.eval().shape == (2, 20, 20, 40, 10)\n", " \n" ] } ], "source": [ "print(pm.Minibatch.__doc__)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pandas 1.0.4\n", "pymc3 3.9.0\n", "theano 1.0.4\n", "numpy 1.18.5\n", "seaborn 0.10.1\n", "last updated: Mon Jun 15 2020 \n", "\n", "CPython 3.7.7\n", "IPython 7.15.0\n", "watermark 2.0.2\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -n -u -v -iv -w" ] } ], "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": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 4 }