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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Neural Networks in PyMC3 estimated with Variational Inference\n",
"(c) 2016 by Thomas Wiecki"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Current trends in Machine Learning\n",
"\n",
"There are currently three big trends in machine learning: **Probabilistic Programming**, **Deep Learning** and \"**Big Data**\". Inside of PP, a lot of innovation is in making things scale using **Variational Inference**. In this blog post, I will show how to use **Variational Inference** in [PyMC3](http://pymc-devs.github.io/pymc3/) to fit a simple Bayesian Neural Network. I will also discuss how bridging Probabilistic Programming and Deep Learning can open up very interesting avenues to explore in future research.\n",
"\n",
"### Probabilistic Programming at scale\n",
"**Probabilistic Programming** allows very flexible creation of custom probabilistic models and is mainly concerned with **insight** and learning from your data. The approach is inherently **Bayesian** so we can specify **priors** to inform and constrain our models and get uncertainty estimation in form of a **posterior** distribution. Using [MCMC sampling algorithms](http://twiecki.github.io/blog/2015/11/10/mcmc-sampling/) we can draw samples from this posterior to very flexibly estimate these models. [PyMC3](http://pymc-devs.github.io/pymc3/) and [Stan](http://mc-stan.org/) are the current state-of-the-art tools to consruct and estimate these models. One major drawback of sampling, however, is that it's often very slow, especially for high-dimensional models. That's why more recently, **variational inference** algorithms have been developed that are almost as flexible as MCMC but much faster. Instead of drawing samples from the posterior, these algorithms instead fit a distribution (e.g. normal) to the posterior turning a sampling problem into and optimization problem. [ADVI](http://arxiv.org/abs/1506.03431) -- Automatic Differentation Variational Inference -- is implemented in [PyMC3](http://pymc-devs.github.io/pymc3/) and [Stan](http://mc-stan.org/), as well as a new package called [Edward](https://github.com/blei-lab/edward/) which is mainly concerned with Variational Inference. \n",
"\n",
"Unfortunately, when it comes to traditional ML problems like classification or (non-linear) regression, Probabilistic Programming often plays second fiddle (in terms of accuracy and scalability) to more algorithmic approaches like [ensemble learning](https://en.wikipedia.org/wiki/Ensemble_learning) (e.g. [random forests](https://en.wikipedia.org/wiki/Random_forest) or [gradient boosted regression trees](https://en.wikipedia.org/wiki/Boosting_(machine_learning)).\n",
"\n",
"### Deep Learning\n",
"\n",
"Now in its third renaissance, deep learning has been making headlines repeatadly by dominating almost any object recognition benchmark, [kicking ass at Atari games](https://www.cs.toronto.edu/~vmnih/docs/dqn.pdf), and [beating the world-champion Lee Sedol at Go](http://www.nature.com/nature/journal/v529/n7587/full/nature16961.html). From a statistical point, Neural Networks are extremely good non-linear function approximators and representation learners. While mostly known for classification, they have been extended to unsupervised learning with [AutoEncoders](https://arxiv.org/abs/1312.6114) and in all sorts of other interesting ways (e.g. [Recurrent Networks](https://en.wikipedia.org/wiki/Recurrent_neural_network), or [MDNs](http://cbonnett.github.io/MDN_EDWARD_KERAS_TF.html) to estimate multimodal distributions). Why do they work so well? No one really knows as the statistical properties are still not fully understood.\n",
"\n",
"A large part of the innoviation in deep learning is the ability to train these extremely complex models. This rests on several pillars:\n",
"* Speed: facilitating the GPU allowed for much faster processing.\n",
"* Software: frameworks like [Theano](http://deeplearning.net/software/theano/) and [TensorFlow](https://www.tensorflow.org/) allow flexible creation of abstract models that can then be optimized and compiled to CPU or GPU.\n",
"* Learning algorithms: training on sub-sets of the data -- stochastic gradient descent -- allows us to train these models on massive amounts of data. Techniques like drop-out avoid overfitting.\n",
"* Architectural: A lot of innovation comes from changing the input layers, like for convolutional neural nets, or the output layers, like for [MDNs](http://cbonnett.github.io/MDN_EDWARD_KERAS_TF.html).\n",
"\n",
"### Bridging Deep Learning and Probabilistic Programming\n",
"On one hand we Probabilistic Programming which allows us to build rather small and focused models in a very principled and well-understood way to gain insight into our data; on the other hand we have deep learning which uses many heuristics to train huge and highly complex models that are amazing at prediction. Recent innovations in variational inference allow probabilistic programming to scale model complexity as well as data size. We are thus at the cusp of being able to combine these two approaches to hopefully unlock new innovations in Machine Learning. For more motivation, see also [Dustin Tran's](https://twitter.com/dustinvtran) recent [blog post](http://dustintran.com/blog/a-quick-update-edward-and-some-motivations/).\n",
"\n",
"While this would allow Probabilistic Programming to be applied to a much wider set of interesting problems, I believe this bridging also holds great promise for innovations in Deep Learning. Some ideas are:\n",
"* **Uncertainty in predictions**: As we will see below, the Bayesian Neural Network informs us about the uncertainty in its predictions. I think uncertainty is an underappreciated concept in Machine Learning as it's clearly important for real-world applications. But it could also be useful in training. For example, we could train the model specifically on samples it is most uncertain about.\n",
"* **Uncertainty in representations**: We also get uncertainty estimates of our weights which could inform us about the stability of the learned representations of the network.\n",
"* **Regularization with priors**: Weights are often L2-regularized to avoid overfitting, this very naturally becomes a Gaussian prior for the weight coefficients. We could, however, imagine all kinds of other priors, like spike-and-slab to enforce sparsity (this would be more like using the L1-norm).\n",
"* **Transfer learning with informed priors**: If we wanted to train a network on a new object recognition data set, we could bootstrap the learning by placing informed priors centered around weights retrieved from other pre-trained networks, like [GoogLeNet](https://arxiv.org/abs/1409.4842). \n",
"* **Hierarchical Neural Networks**: A very powerful approach in Probabilistic Programming is hierarchical modeling that allows pooling of things that were learned on sub-groups to the overall population (see my tutorial on [Hierarchical Linear Regression in PyMC3](http://twiecki.github.io/blog/2014/03/17/bayesian-glms-3/)). Applied to Neural Networks, in hierarchical data sets, we could train individual neural nets to specialize on sub-groups while still being informed about representations of the overall population. For example, imagine a network trained to classify car models from pictures of cars. We could train a hierarchical neural network where a sub-neural network is trained to tell apart models from only a single manufacturer. The intuition being that all cars from a certain manufactures share certain similarities so it would make sense to train individual networks that specialize on brands. However, due to the individual networks being connected at a higher layer, they would still share information with the other specialized sub-networks about features that are useful to all brands. Interestingly, different layers of the network could be informed by various levels of the hierarchy -- e.g. early layers that extract visual lines could be identical in all sub-networks while the higher-order representations would be different. The hierarchical model would learn all that from the data.\n",
"* **Other hybrid architectures**: We can more freely build all kinds of neural networks. For example, Bayesian non-parametrics could be used to flexibly adjust the size and shape of the hidden layers to optimally scale the network architecture to the problem at hand during training. Currently, this requires costly hyper-parameter optimization and a lot of tribal knowledge."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bayesian Neural Networks in PyMC3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generating data\n",
"\n",
"First, lets generate some toy data -- a simple binary classification problem that's not linearly separable."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import pymc3 as pm\n",
"import theano.tensor as T\n",
"import theano\n",
"import sklearn\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set_style('white')\n",
"from sklearn import datasets\n",
"from sklearn.preprocessing import scale\n",
"from sklearn.cross_validation import train_test_split\n",
"from sklearn.datasets import make_moons\n",
"\n",
"import lasagne"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"X, Y = make_moons(noise=0.2, random_state=0, n_samples=1000)\n",
"X = scale(X)\n",
"X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.5)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
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OgwcPir5zOBz49ttvRd8lJiZi6dKlSEpKwnfffYfz58/j9ttvx5///GcsWLAAF154IZYs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\nmdEx8xOqkBCPcfS2cwxGyMqZw6WLBo8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upLGYglLlttRUeQtRe7v489/+xv2rFO+hpzKg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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f61f707c470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.scatter(X[Y==0, 0], X[Y==0, 1], label='Class 0')\n",
"ax.scatter(X[Y==1, 0], X[Y==1, 1], color='r', label='Class 1')\n",
"sns.despine(); ax.legend()\n",
"ax.set(xlabel='X', ylabel='Y', title='Toy binary classification data set');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model specification\n",
"\n",
"A neural network is quite simple. The basic unit is a [perceptron](https://en.wikipedia.org/wiki/Perceptron) which is nothing more than [logistic regression](http://pymc-devs.github.io/pymc3/notebooks/posterior_predictive.html#Prediction). We use many of these in parallel and then stack them up to get hidden layers. Here we will use 2 hidden layers with 5 neurons each which is sufficient for such a simple problem."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Trick: Turn inputs and outputs into shared variables. \n",
"# It's still the same thing, but we can later change the values of the shared variable \n",
"# (to switch in the test-data later) and pymc3 will just use the new data. \n",
"# Kind-of like a pointer we can redirect.\n",
"# For more info, see: http://deeplearning.net/software/theano/library/compile/shared.html\n",
"ann_input = theano.shared(X_train)\n",
"ann_output = theano.shared(Y_train)\n",
"\n",
"n_hidden = 5\n",
"\n",
"# Initialize random weights between each layer\n",
"init_1 = np.random.randn(X.shape[1], n_hidden)\n",
"init_2 = np.random.randn(n_hidden, n_hidden)\n",
"init_out = np.random.randn(n_hidden, 1)\n",
" \n",
"with pm.Model() as neural_network:\n",
" # Weights from input to hidden layer\n",
" weights_in_1 = pm.Normal('w_in_1', 0, sd=1, \n",
" shape=(X.shape[1], n_hidden), \n",
" testval=init_1)\n",
" \n",
" # Weights from 1st to 2nd layer\n",
" weights_1_2 = pm.Normal('w_1_2', 0, sd=1, \n",
" shape=(n_hidden, n_hidden), \n",
" testval=init_2)\n",
" \n",
" # Weights from hidden layer to output\n",
" weights_2_out = pm.Normal('w_2_out', 0, sd=1, \n",
" shape=(n_hidden, 1), \n",
" testval=init_out)\n",
" \n",
" # Build neural-network using tanh activation function\n",
" act_in = lasagne.layers.InputLayer(X_train.shape, \n",
" input_var=ann_input)\n",
" \n",
" act_1 = lasagne.layers.DenseLayer(act_in, n_hidden, \n",
" W=weights_in_1, \n",
" nonlinearity=lasagne.nonlinearities.tanh)\n",
" act_2 = lasagne.layers.DenseLayer(act_1, n_hidden, \n",
" W=weights_1_2, \n",
" nonlinearity=lasagne.nonlinearities.tanh)\n",
" act_out = lasagne.layers.DenseLayer(act_2, 1, \n",
" W=weights_2_out,\n",
" nonlinearity=lasagne.nonlinearities.sigmoid)\n",
" \n",
" net_out = lasagne.layers.get_output(act_out)\n",
" \n",
" # Binary classification -> Bernoulli likelihood\n",
" out = pm.Bernoulli('out', \n",
" net_out.flatten(),\n",
" observed=ann_output)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's not so bad. The `Normal` priors help regularize the weights. Usually we would add a constant `b` to the inputs but I omitted it here to keep the code cleaner."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Variational Inference: Scaling model complexity\n",
"\n",
"We could now just run a MCMC sampler like [`NUTS`](http://pymc-devs.github.io/pymc3/api.html#nuts) which works pretty well in this case but as I already mentioned, this will become very slow as we scale our model up to deeper architectures with more layers.\n",
"\n",
"Instead, we will use the brand-new [ADVI](http://pymc-devs.github.io/pymc3/api.html#advi) variational inference algorithm which was recently added to `PyMC3`. This is much faster and will scale better. Note, that this is a mean-field approximation so we ignore correlations in the posterior."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration 0 [0%]: ELBO = -657.22\n",
"Iteration 5000 [10%]: ELBO = -282.21\n",
"Iteration 10000 [20%]: ELBO = -211.17\n",
"Iteration 15000 [30%]: ELBO = -225.02\n",
"Iteration 20000 [40%]: ELBO = -254.61\n",
"Iteration 25000 [50%]: ELBO = -225.2\n",
"Iteration 30000 [60%]: ELBO = -205.56\n",
"Iteration 35000 [70%]: ELBO = -165.1\n",
"Iteration 40000 [80%]: ELBO = -146.27\n",
"Iteration 45000 [90%]: ELBO = -178.99\n",
"Finished [100%]: ELBO = -123.47\n",
"CPU times: user 22.3 s, sys: 384 ms, total: 22.7 s\n",
"Wall time: 25.1 s\n"
]
}
],
"source": [
"%%time\n",
"\n",
"with neural_network:\n",
" # Run ADVI which returns posterior means, standard deviations, and the evidence lower bound (ELBO)\n",
" v_params = pm.variational.advi(n=50000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"< 40 seconds on my older laptop. That's pretty good considering that NUTS is having a really hard time. Further below we make this even faster. To make it really fly, we probably want to run the Neural Network on the GPU.\n",
"\n",
"As samples are more convenient to work with, we can very quickly draw samples from the variational posterior using `sample_vp()` (this is just sampling from Normal distributions, so not at all the same like MCMC):"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with neural_network:\n",
" trace = pm.variational.sample_vp(v_params, draws=5000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotting the objective function (ELBO) we can see that the optimization slowly improves the fit over time."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f61cebcf8d0>"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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iozWj6n19+sieeDS6vahtzRgdZnDGSz9PJ/z99WSonBUYEBWIyO6+jfayfn58b7w0MQrS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\nojA0EBERkSgMDURERCTK/wf+0euzoEi2vQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f61cc8c0d68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(v_params.elbo_vals)\n",
"plt.ylabel('ELBO')\n",
"plt.xlabel('iteration')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we trained our model, lets predict on the hold-out set using a posterior predictive check (PPC). We use [`sample_ppc()`](http://pymc-devs.github.io/pymc3/api.html#pymc3.sampling.sample_ppc) to generate new data (in this case class predictions) from the posterior (sampled from the variational estimation)."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Replace shared variables with testing set\n",
"ann_input.set_value(X_test)\n",
"ann_output.set_value(Y_test)\n",
"\n",
"# Creater posterior predictive samples\n",
"ppc = pm.sample_ppc(trace, model=neural_network, samples=500)\n",
"\n",
"# Use probability of > 0.5 to assume prediction of class 1\n",
"pred = ppc['out'].mean(axis=0) > 0.5"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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gaW7+AB0doTnTUmANBjvR3d0Fv/8RHDuWhTNnMgAUQy3w6j1nelqtakFRb09D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\nHvX/ATba0XaWxqUTAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f61cbf9eeb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
"ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
"sns.despine()\n",
"ax.set(title='Predicted labels in testing set', xlabel='X', ylabel='Y');"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Accuracy = 96.6%\n"
]
}
],
"source": [
"print('Accuracy = {}%'.format((Y_test == pred).mean() * 100))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Hey, our neural network did all right!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lets look at what the classifier has learned\n",
"\n",
"For this, we evaluate the class probability predictions on a grid over the whole input space."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"grid = np.mgrid[-3:3:100j,-3:3:100j]\n",
"grid_2d = grid.reshape(2, -1).T\n",
"dummy_out = np.ones(grid.shape[1], dtype=np.int8)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ann_input.set_value(grid_2d)\n",
"ann_output.set_value(dummy_out)\n",
"\n",
"# Creater posterior predictive samples\n",
"ppc = pm.sample_ppc(trace, model=neural_network, samples=500)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Probability surface"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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g59evX8/rPCSICNGE2/A00MOTSvNEEzT4GoA0hlk5yrLFzitjjsmI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\nc0SCq/miVKkyoewakIuctraAey00Qic3VEpPxBvr16+Paj0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9Q8kShuQS6009MCCIHXKT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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f61cb8b6c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmap = sns.diverging_palette(250, 12, s=85, l=25, as_cmap=True)\n",
"fig, ax = plt.subplots(figsize=(10, 6))\n",
"contour = ax.contourf(*grid, ppc['out'].mean(axis=0).reshape(100, 100), cmap=cmap)\n",
"ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
"ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
"cbar = plt.colorbar(contour, ax=ax)\n",
"_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n",
"cbar.ax.set_ylabel('Posterior predictive mean probability of class label = 0');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Uncertainty in predicted value\n",
"\n",
"So far, everything I showed we could have done with a non-Bayesian Neural Network. The mean of the posterior predictive for each class-label should be identical to maximum likelihood predicted values. However, we can also look at the standard deviation of the posterior predictive to get a sense for the uncertainty in our predictions. Here is what that looks like:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Px5o1a5Cdne2zzZNPPolhw4YhPz8fOTne16Py8nK88847eP/99/Hss8+KHmPQCSIzXRCl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\naiEyEqMyxtSYlvnVp6vP9EJuSQEeerCiS/A0ovL4n/GPynPwph1Fju9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k7Aw0kqa9HX0K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\nKJSEhwoiCoVCoVAoCc//ByLybuvlLKPNAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f61c91e8ac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmap = sns.cubehelix_palette(light=1, as_cmap=True)\n",
"fig, ax = plt.subplots(figsize=(10, 6))\n",
"contour = ax.contourf(*grid, ppc['out'].std(axis=0).reshape(100, 100), cmap=cmap)\n",
"ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
"ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
"cbar = plt.colorbar(contour, ax=ax)\n",
"_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n",
"cbar.ax.set_ylabel('Uncertainty (posterior predictive standard deviation)');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that very close to the decision boundary, our uncertainty as to which label to predict is highest. You can imagine that associating predictions with uncertainty is a critical property for many applications like health care. To further maximize accuracy, we might want to train the model primarily on samples from that high-uncertainty region."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mini-batch ADVI: Scaling data size\n",
"\n",
"So far, we have trained our model on all data at once. Obviously this won't scale to something like ImageNet. Moreover, training on mini-batches of data (stochastic gradient descent) avoids local minima and can lead to faster convergence.\n",
"\n",
"Fortunately, ADVI can be run on mini-batches as well. It just requires some setting up:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Set back to original data to retrain\n",
"ann_input.set_value(X_train)\n",
"ann_output.set_value(Y_train)\n",
"\n",
"# Tensors and RV that will be using mini-batches\n",
"minibatch_tensors = [ann_input, ann_output]\n",
"minibatch_RVs = [out]\n",
"\n",
"# Generator that returns mini-batches in each iteration\n",
"def create_minibatch(data):\n",
" rng = np.random.RandomState(0)\n",
" \n",
" while True:\n",
" # Return random data samples of set size 100 each iteration\n",
" ixs = rng.randint(len(data), size=50)\n",
" yield data[ixs]\n",
"\n",
"minibatches = [\n",
" create_minibatch(X_train), \n",
" create_minibatch(Y_train),\n",
"]\n",
"\n",
"total_size = len(Y_train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While the above might look a bit daunting, I really like the design. Especially the fact that you define a generator allows for great flexibility. In principle, we could just pool from a database there and not have to keep all the data in RAM. \n",
"\n",
"Lets pass those to `advi_minibatch()`:"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration 0 [0%]: ELBO = -311.63\n",
"Iteration 5000 [10%]: ELBO = -162.34\n",
"Iteration 10000 [20%]: ELBO = -70.49\n",
"Iteration 15000 [30%]: ELBO = -153.64\n",
"Iteration 20000 [40%]: ELBO = -164.07\n",
"Iteration 25000 [50%]: ELBO = -135.05\n",
"Iteration 30000 [60%]: ELBO = -240.99\n",
"Iteration 35000 [70%]: ELBO = -111.71\n",
"Iteration 40000 [80%]: ELBO = -87.55\n",
"Iteration 45000 [90%]: ELBO = -97.5\n",
"Finished [100%]: ELBO = -75.31\n",
"CPU times: user 17.4 s, sys: 56 ms, total: 17.5 s\n",
"Wall time: 17.5 s\n"
]
}
],
"source": [
"%%time\n",
"\n",
"with neural_network:\n",
" # Run advi_minibatch\n",
" v_params = pm.variational.advi_minibatch(\n",
" n=50000, minibatch_tensors=minibatch_tensors, \n",
" minibatch_RVs=minibatch_RVs, minibatches=minibatches, \n",
" total_size=total_size, learning_rate=1e-2, epsilon=1.0\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with neural_network: \n",
" trace = pm.variational.sample_vp(v_params, draws=5000)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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tdfl7u+DmnQeQ1bLGq9WlaQRsznMvqGoYGkRa+VoiZv5jLwqKSi26XmNPSBvR\nJwwbvq5+Q6LyVypymQOKStQAyu5hGiJ3lGL8oIhqb9uSNi16stqhwdr3VP29nHFT5PgWoph5kTnR\njKco1mWaz7X8iJCWVNk3r22oPzq0tvzQ55b2/rQkPCwsqfJw27Vdj/YNceP2A5OjqpJlMDSIFNrQ\nC1uX9KvQuK66jF1IDOneAlt2nUHxXyf48qJa+IuqadC1/a3+uJKjwisrfqpqMS2mnrcLcvMK4VnF\n++lVbVQIAOMHReD67Xx0DA/EwVPX0SxYv4FXv85N8OWe81VerzEfpnVHSSXdUGuustl+DO3RArfv\nFWC4FRp2Ln25MzZ+m1Vp11VHmUOlbWo+mdvLqsFGDEeZAxxlFhqBqBZxlEnxggVGzqTKMTSIoPsg\nk0BfV1y7lV/pMq2aeOPU+cpP6hKJBI0C3HDxep522nN9yoYPNnV180z3UMSE+ePAyev47PszRudL\n0hkf31HmgCBfV8ikDujX2XL99zUPTBFz9TJtZDv8377zGNytObb/fNZiZTBE90BvaIS7Dq0DLBoa\npFIHSG17TrBLHkonsx4EJEbrpj4WG4nPq5pDWBPVBo9XHZUFaU4yDeq5Vfro5SeiKj7LIMjX/HvK\nz3QPBVDWEMpFYTjXSR0kCG3ohef6tMRAA0+dbN8qADuWJyO0of4T5+SOUmx/q5/eI5GrKzmhKaJb\n+GPxxMoPrr6ezhj5ZCs4O8nMat9gSbbePhFRXcPQYISx6vMX+lWsAqvw+FaR/rvc8DPYNaLD/LFu\nTq9K1zO8dxg6tA7A5GH6vSQcjA6VbNlGUEoXOeaPjRP9GGlrl6c2s/U71fQ/t/bjc83HJEdUm9XW\nI4dNmXq2QlybQOxckYzkVP1xElZP7QoHiQQTl/0I4NHQqb6ezvhodk/cvPMAC/99ABeu3dcuoxl+\nt1tsQ+1DdMrXGiicZFgwNg71fIwPKqOQyzDrxQ7IzXs0vHCAb+0bhKa2qaunp+WvJlQ6eqQx709P\ngupBMZwceR+FiKqOocEAd6WTyfHSDV0ZNwow3AtCM6u/twveS+2qbUi5bu6jGoSnujRDYlR9o7dB\nxD4xUnccghG9K3+sMtVN5tboAJon8dX9nz1vLRE9ktKtOe7cL6h8Rguo+0cPa9A5IFmr5txbp1GU\nRCKptN2EGB5KOXp1bISIEF/tAE1kAk88dZ6tnxFAVBs837dVjW2LZxYL+2ReLzg5SvHhf4/X+LYl\nEonBAWJoueUfAAAa10lEQVRqK28PBW7eeWC0sSfZI4YAotqMDSHN9EGa4ceyerkp4KJwZPWpCAvG\nxqFffBP072yboWWt9cheMp+jzAGDu4bgzedibV0UIjKAl3hGVHbSD/JVaodkNYXXTcbV91NiXC0b\nedIadL9LHn8NcxsRYpmHAj2ORhnooUREtQNDgyESg39aRI/2DY12haSaZYvaICdHKbYu6cveC9XU\nLbYB1n11Ch3CA2xdFCK7wtBgbeVaUr46pGpPnKTHz+PQe8HWBncNwRNRwfDzqn4DYiISj20arGRQ\nlxAo5FJMHPz4V7/XVS0alY2WWVsf3Szhr9MoiUTCwEBkA7zksZJGge7YuqSfrYtBJri5yLFzRXKt\nHZGyfasARIf526yhKBFReQwNBkgkZQMq/XL8Gjq2Mfz4aLKOJRPjzR7t0By1NTAAZc8JmT8mztbF\nICLSYmgwonfHRmjZ2BsN6rnZuih2JbwZexUQEdVWDA1GSCQSNA40PDQ0UVVwPAgielywqRURERGJ\nwtBQDZF/DdDTrL6HjUtCRERkfbw9YYDYpnFjn2qDThFBiAr1s2p5iIiIagPWNPwltmW9Ki+jkMsQ\n27IepDXY2p+IiMhWak1NQ2JiIho3bgwAiIqKwuTJk3HkyBEsXrwYMpkMnTp1wqRJkwAAq1evxu7d\nuyGTyZCWloaIiOoPoDS8dxgO/X6j2ushIiJ6XNWK0HDp0iW0bt0a//jHP/Smz5s3D6tXr0ZwcDDG\njh2LrKwsqNVqHDp0CFu3bsW1a9fwyiuvYNu2bdUvBBu4ExERmVQrQsOJEydw48YNjBw5Es7OzkhL\nS4Ovry+Ki4sRHBwMAOjcuTP27t0LuVyO+Ph4AEBgYCDUajVyc3Ph5eVVrTKwWxxZi4TPOiWix0SN\nh4Zt27Zh3bp1etPmzp2LcePGoVevXsjMzERqairWrFkDpVKpncfV1RXZ2dlQKBTw9PTUTndxcYFK\npap2aNBTi0cJpLrHQylHj/YNEdGcDWaJqG6r8dCQkpKClJQUvWkFBQWQSsseFRwTE4OcnBy4urpC\npVJp58nPz4eHhwccHR2Rn5+vN93NrfqjNtriMclkHyQSCZ9uSkSPhVrR7H/16tXa2oesrCwEBgZC\nqVRCLpcjOzsbgiBgz549iImJQVRUFPbs2QNBEHD16lUIgqBX80BERETWUSvaNIwdOxZTp07V9ohY\nsmQJgLKGkKmpqVCr1YiPj9f2koiJicGQIUMgCALmzJljy6ITERHZjVoRGtzd3fHBBx9UmB4ZGYkt\nW7ZUmD5p0iRt90trYIsGIiKiimrF7YnaQGCjBiIiIpMYGoiIiEgUhoa/sJ6BiIjINIYGIiIiEoWh\n4S9OjlLt3xzbiYiIqCKGBgDjn2qDYP/qDxBFRET0OKsVXS5t6fm+rdC3c1NbF4OIiKjWY02Djugw\nf1sXgYiIqNZiaNAxoncYXBUyvNg/3NZFISIiqnXs/vaEbpvH5g28sDm9r83KQkREVJvZfU0De0oQ\nERGJY/ehgYiIiMRhaCAiIiJRGBr4TEsiIiJRGBqIiIhIFIYGIiIiEsXuQ0PPjo1sXQQiIqI6we5D\ng9LZ0dZFICIiqhPsPjQQERGROAwNREREJApDAxEREYnC0EBERESiMDQQERGRKAwNREREJApDAxER\nEYnC0EBERESiMDQQERGRKAwNREREJApDAxEREYnC0EBERESiMDQQERGRKAwNREREJApDAxEREYnC\n0EBERESiMDQQERGRKAwNREREJApDAxEREYkis3UBbKVLdDD6dm5i62IQERHVGXYbGqYMj7F1EYiI\niOoU3p4gIiIiURgaiIiISBSGBiIiIhKFoYGIiIhEYWggIiIiURgaiIiISBSGBiIiIhKFoYGIiIhE\nYWggIiIiURgaiIiISBSGBiIiIhKFoYGIiIhEYWggIiIiURgaiIiISBSGBiIiIhKFoYGIiIhEYWgg\nIiIiURgaiIiISBSGBiIiIhKFoYGIiIhEYWggIiIiURgaiIiISBRZZTMUFRXhm2++wfHjxwEAbdq0\nQe/evSGXy61eOCIiIqo9TNY05ObmYvDgwVi/fj1kMhkEQcAnn3yCwYMHIzc3t6bKSERERLWAyZqG\n5cuXo3///hg7dqze9L///e9Yvnw5Fi9ebNXCERERUe1hsqbh+PHjFQIDAEycOBGZmZlWKxQRERHV\nPiZDQ3FxsdHXpFKpxQtDREREtZfJ0FCvXj3s37+/wvRffvkFgYGBVisUERER1T4m2zRMmTIFEydO\nxNChQxEREYHS0lL89ttv2L59O/71r3/VVBmJiIioFjAZGiIiIvDxxx9j7dq1+OabbyCRSBAREYGN\nGzeiYcOGNVVGIiIiqgUqHachJCQES5YssfiGd+3ahW+++QYrV64EABw9ehTp6emQyWTo1KkTJk2a\nBABYvXo1du/eDZlMhrS0NERERCA3NxepqakoLCyEv78/lixZAicnJ4uXkYiIiB4x2aahqKgImzZt\nwvfffw+VSoXRo0cjOjoazz33HM6fP2/2RtPT0/HOO+/oTZs7dy7efvttbNy4EceOHUNWVhZOnTqF\nQ4cOYevWrXj77bexYMECAMCaNWvQv39/bNiwAWFhYdi0aZPZZSEiIiJxTIaGGTNmYN++fdi8eTNG\njBiBli1bYuPGjejWrRvmzJlj9kajo6Mxb9487f8qlQrFxcUIDg4GAHTu3Bl79+5FZmYm4uPjAQCB\ngYFQq9W4c+cODh8+jISEBABAYmKiwcaaREREZFkmb09kZWXhyy+/RFFRERITE5GamgoACAsLw+ef\nf17pyrdt24Z169bpTVuyZAn69OmDX3/9VTstPz8fSqVS+7+rqyuys7OhUCjg6empN12lUiE/Px9u\nbm7aaXl5eSLeKhEREVWHydAgk5W9LJfLERAQYPA1U1JSUpCSklLpfJowoJGfnw8PDw84OjoiPz9f\nO12lUsHd3V07v7e3t16AICIiIusxeXtCIpEY/NvQ/9WhVCohl8uRnZ0NQRCwZ88exMTEICoqCnv2\n7IEgCLh69SoEQYCnpyeio6ORkZEBAMjIyEBsbKzFykJERESGmawu+P3339GyZUsAgCAIen9bMjQA\nwPz585Gamgq1Wo34+HhEREQAAGJiYjBkyBAIgqBtRzFhwgRMmzYNn332Gby8vLQ9MIiIiMh6JIIg\nCLYuhLVdvnwZSUlJaNJtOhxdvAEAX6wcYONSERER1S0mb0+Y0r9/f0uWg4iIiGo5s0PD5cuXLVkO\nIiIiquXMDg2WbtNAREREtZvZoYGIiIjsi8neE2FhYQZrFKzRe4KIiIhqN5OhYfbs2Rg+fDgA4MyZ\nMwgNDdW+tmjRIuuWjIiIiGoVk7cntm3bpv172rRpeq9lZmZap0RERERUK5kMDbpDOJQfzsEOhncg\nIiIiHaIbQlpzGGkiIiKq/UQ/e4KIiIjsm8mGkH/88QeSkpIAADdu3ND+LQgCcnJyrF86IiIiqjVM\nhoZvv/22pspBREREtZzJ0FC/fv2aKgcRERHVchwRkoiIiERhaCAiIiJRGBqIiIhIFIYGIiIiEoWh\ngYiIiERhaCAiIiJRGBqIiIhIFIYGIiIiEoWhgYiIiESxy9AwZkC4rYtARERU59hlaAjwcbV1EYiI\niOocuwwNgiDYughERER1jl2GBiIiIqo6hgYiIiIShaGBiIiIRGFoICIiIlEYGoiIiEgUuwwN7DtB\nRERUdXYZGoiIiKjqGBqIiIhIFIYGIiIiEoWhgYiIiERhaCAiIiJRGBqIiIhIFLsMDc0beNq6CERE\nRHWOXYYGHw9nWxeBiIiozrHL0EBERERVZ3ehQe4otXURiIiI6iS7Cw1jB4bbughERER1kt2FBiIi\nIjKPHYYGia0LQEREVCfZYWggIiIiczA0EBERkSgMDURERCQKQwMRERGJwtBAREREojA0EBERkSgM\nDURERCQKQwMRERGJwtBAREREothdaJBwQEgiIiKz2F1oICIiIvMwNBAREZEoDA1EREQkit2FBkGw\ndQmIiIjqJrsLDURERGQehgYiIiIShaGBiIiIRGFoICIiIlEYGoiIiEgUuwsNHBGSiIjIPHYXGoiI\niMg8DA1EREQkCkMDERERicLQQERERKLYLDTs2rULU6ZM0f7//fffo0ePHhg5ciRGjhyJQ4cOAQBW\nr16Np59+GsOGDcOxY8cAALm5uRg9ejRGjBiBN954A4WFhTZ5D0RERPZEZouNpqenY+/evWjZsqV2\n2okTJ/Dmm2+iR48e2mmnTp3CoUOHsHXrVly7dg2vvPIKtm3bhjVr1qB///4YOHAgPvzwQ2zatAmj\nRo2ywTshIiKyHzapaYiOjsa8efP0pp08eRKff/45hg8fjrfeegulpaXIzMxEfHw8ACAwMBBqtRp3\n7tzB4cOHkZCQAABITEzE/v37a/otEBER2R2r1jRs27YN69at05u2ZMkS9OnTB7/++qve9Pj4eHTv\n3h3BwcGYO3cuNm/eDJVKBS8vL+08rq6uUKlUyM/Ph5ubm3ZaXl6eNd8GERERwcqhISUlBSkpKaLm\nHTx4sDYIdOvWDd999x1atmwJlUqlnUelUsHd3V0bHry9vfUCBBEREVlPrek9kZycjBs3bgAA9u/f\nj/DwcERFRWHv3r0QBAFXr16FIAjw9PREdHQ0MjIyAAAZGRmIjY0VvR0OCElERGQemzSENCQ9PR2T\nJk2CQqFASEgInnnmGUilUsTExGDIkCEQBAFz5swBAEyYMAHTpk3DZ599Bi8vL6xcudLGpSciInr8\nSQRBEGxdCGu7fPkykpKS0KTbdEwZ1Q09OjSydZGIiIjqnFpze4KIiIhqN4YGIiIiEoWhgYiIiERh\naCAiIiJRGBqIiIhIFIYGIiIiEoWhgYiIiESxu9Ag4ZCQREREZrG70EBERETmYWggIiIiURgaiIiI\nSBSGBiIiIhKFoYGIiIhEYWggIiIiURgaiIiISBSGBiIiIhKFoYGIiIhEscPQwCEhiYiIzGGHoYGI\niIjMwdBAREREojA0EBERkSgMDURERCQKQwMRERGJwtBAREREojA0EBERkSgMDURERCQKQwMRERGJ\nYnehQcIBIYmIiMxid6GBiIiIzMPQQERERKIwNBAREZEoDA1EREQkCkMDERERicLQQERERKIwNBAR\nEZEoDA1EREQkCkMDERERiWJ3oYEjQhIREZnH7kIDERERmYehgYiIiERhaCAiIiJRGBqIiIhIFIYG\nIiIiEoWhgYiIiERhaCAiIiJRGBqIiIhIFIYGIiIiEsUOQwOHhCQiIjKHHYYGIiIiMgdDAxEREYnC\n0EBERESiMDQQERGRKAwNREREJApDAxEREYnC0EBERESiMDQQERGRKHYXGtqG+tm6CERERHWSXYWG\nf87oDm93ha2LQUREVCfZVWiQSDiENBERkbnsKjQQERGR+RgaiIiISBSGBiIiIhKFoYGIiIhEYWgg\nIiIiURgaiIiISBSGBiIiIhKFoYGIiIhEYWggIiIiURgaiIiISBRZTW9QpVIhNTUV+fn5KC4uRlpa\nGiIjI3HkyBEsXrwYMpkMnTp1wqRJkwAAq1evxu7duyGTyZCWloaIiAjk5uYiNTUVhYWF8Pf3x5Il\nS+Dk5FTTb4WIiMiu1HhNw0cffYROnTph/fr1WLJkCebPnw8AmDdvHt5++21s3LgRx44dQ1ZWFk6d\nOoVDhw5h69atePvtt7FgwQIAwJo1a9C/f39s2LABYWFh2LRpU02/DSIiIrtT46HhhRdewNChQwEA\nJSUlcHJygkqlQnFxMYKDgwEAnTt3xt69e5GZmYn4+HgAQGBgINRqNe7cuYPDhw8jISEBAJCYmIj9\n+/fX9NsgIiKyO1a9PbFt2zasW7dOb9qSJUsQHh6OnJwcvPnmm5g5cyby8/OhVCq187i6uiI7OxsK\nhQKenp5601UqFfLz8+Hm5qadlpeXZ7IcpaWlAIDr169b6q0RERHVegEBAZDJLHeqt2poSElJQUpK\nSoXpp0+fRmpqKqZNm4bY2FioVCqoVCrt6/n5+fDw8ICjoyPy8/O101UqFdzd3bXhwdvbWy9AGJOT\nkwMAGD58uIXeGRERUe33ww8/aGvxLaHGG0KePXsWr7/+OlatWoUWLVoAAJRKJeRyObKzsxEcHIw9\ne/Zg0qRJkEqlWLFiBV588UVcu3YNgiDA09MT0dHRyMjIwMCBA5GRkYHY2FiT2wwPD8enn34KPz8/\nSKXSmnibRERENhcQEGDR9UkEQRAsusZKTJw4EadPn0b9+vUhCALc3d2xZs0aHD16FIsXL4ZarUZ8\nfDxef/11AGW9JzIyMiAIAtLS0hAdHY3bt29j2rRpePDgAby8vLBy5UooFIqafBtERER2p8ZDAxER\nEdVNHNyJiIiIRGFoICIiIlEYGoiIiEgUhgYiIiISpca7XNYkQRAwb948nD59GnK5HOnp6WjQoIGt\ni1VnHD16FCtWrMD69etx6dIlTJ8+HQ4ODmjevDnmzp0LAPjss8+wZcsWODo6Yvz48ejSpQsKCwsx\ndepU3L59G0qlEkuXLoWXl5fR54vYo5KSEsyYMQNXrlxBcXExxo8fj5CQEO5jC1Or1Zg1axbOnz8P\nBwcHzJ8/H3K5nPvZCm7fvo3Bgwfjo48+glQq5T62sEGDBmkHQQwODsb48eNts4+Fx9h3330nTJ8+\nXRAEQThy5IgwYcIEG5eo7vjnP/8p9OvXTxgyZIggCIIwfvx44eDBg4IgCMKcOXOEXbt2CTk5OUK/\nfv2E4uJiIS8vT+jXr59QVFQkfPTRR8J7770nCIIgfPXVV8KiRYsEQRCEAQMGCNnZ2YIgCMKYMWOE\n33//3QbvrHb4/PPPhcWLFwuCIAj37t0TunTpwn1sBbt27RJmzJghCIIgHDhwQJgwYQL3sxUUFxcL\nL7/8stCrVy/h3Llz3McWVlhYKDz11FN602y1jx/r2xOZmZnaZ1RERkbixIkTNi5R3dGoUSOsWbNG\n+//Jkye1g2glJiZi3759OHbsGGJiYiCTyaBUKtG4cWNkZWUhMzMTiYmJ2nn3799v8Pki+/btq/k3\nVkv06dMHr732GoCyYc6lUilOnTrFfWxh3bt3x8KFCwEAV69ehYeHB/ezFbz11lsYNmwY/P39IQgC\n97GFZWVl4cGDBxg9ejRGjRqFo0eP2mwfP9ahQaVS6Q0xLZPJoFarbViiuqNHjx56o2cKOsN5GHoG\nCAC4uLhop2uq0TTPBjH0fJHKnhnyOHN2dtbur9deew2TJ0/mPrYSBwcHTJ8+HYsWLUK/fv24ny1s\n+/bt8PHxQXx8vHbf6h5nuY+rT6FQYPTo0Vi7di3mzZuH1NRUm32PH+s2DUqlUu/ZFWq1Gg4Oj3VO\nshrd/Zafnw93d3colcoKzwzRTNfsd82XWPOlLj+vPbt27RomTZqEESNGoG/fvli+fLn2Ne5jy1q6\ndClu376NlJQUFBYWaqdzP1ff9u3bIZFIsHfvXpw+fRrTpk1Dbm6u9nXu4+pr3LgxGjVqpP3b09MT\np06d0r5ek/v4sT6DRkdHY/fu3QCAI0eOIDQ01MYlqrtatWqFgwcPAgAyMjIQExODNm3aIDMzE0VF\nRcjLy8O5c+fQvHlzREVFaff77t27ERsbq/d8EUEQsGfPHsTExNjyLdnUrVu3MHr0aEydOhVPPfUU\nAKBly5bcxxa2Y8cOfPjhhwAAJycnODg4IDw8HL/++isA7mdL2LBhA9avX4/169cjLCwMy5YtQ0JC\nAr/LFvT5559j6dKlAIAbN25ApVIhPj7eJt/jx3oYaUGn9wRQ9ljuJk2a2LhUdceVK1cwZcoUbN68\nGRcuXMDs2bNRXFyMZs2aYdGiRZBIJNi6dSu2bNkCQRAwYcIEdO/eHQUFBZg2bRpycnIgl8uxcuVK\n+Pj44NixY0hPT6/wfBF7lJ6ejq+//hpNmzaFIAiQSCSYOXMmFi1axH1sQQ8fPkRaWhpu3bqFkpIS\njBs3Dk2bNsWsWbO4n61g5MiRmD9/PiQSCY8XFlRcXIy0tDRcvXoVDg4OmDp1Kjw9PW3yPX6sQwMR\nERFZzmN9e4KIiIgsh6GBiIiIRGFoICIiIlEYGoiIiEgUhgYiIiIShaGBiIiIRHmsR4QkIvOcOHEC\nW7ZsQZs2baBUKvHkk09We50//fQTLl68iFGjRmHz5s2QSCQYMmSIBUpLRDWFoYGIKggPD0d4eDjS\n0tLQoUMHi6zz5MmT2r+HDh1qkXUSUc1iaCCiCn799VesWrUKf/75Jw4cOAA/Pz+EhYVhzpw5uH79\nOhwcHPDGG28gLi4Oq1evxpEjR3D9+nUMHz4cISEheOedd1BQUID79+9j6tSpCAkJwebNmwEA9evX\nx5UrVwAAkyZNwk8//YR3330XgiCgQYMGWLBgAby9vdGtWzcMGDAAe/bsQUFBAd566y20atXKlruF\nyO4xNBCRQVKpFN26dUOHDh0QHx+PN954AykpKejatStycnLw7LPPYseOHQCAoqIifPnllwCA1157\nDenp6WjSpAn279+PxYsXY+fOndrahaeeegqrV68GANy5cwdz587Fli1bEBgYiLVr12LBggVYtWoV\nAMDb2xtbt27Fhg0b8P777+Nvf/ubDfYEEWkwNBCRKPv27cP58+fx7rvvAgBKS0tx6dIlAEBkZKR2\nvuXLl+Onn37C119/jaNHj+LBgwdG13ns2DFERkYiMDAQADBkyBDtA6YAoHPnzgCA5s2bY9euXRZ/\nT0RUNQwNRCSKIAhYt26d9vG5N2/ehK+vL77//ns4OTlp5xs2bBji4uLQvn17xMXFITU11eg61Wo1\ndB9/o1arUVpaqv1fs16JRAI+JofI9tjlkoiMkslkKCkpAQB06NABn376KQDg7NmzSE5ORkFBgd78\n9+7dw6VLl/Dqq68iMTERe/bsgVqtBlB2u0M3EABlNRRHjx7F1atXAQBbtmxBx44drf22iMhMrGkg\nIoMkEgni4uLwzjvvwN3dHbNnz8bs2bORnJwMAFixYgVcXFz0lvHw8EBKSgr69u0LNzc3tG3bFg8f\nPkRBQQHatWuH6dOnw9fXVzu/j48PFi5ciJdffhklJSUICgpCenq6dvtEVLvw0dhEREQkCm9PEBER\nkSgMDURERCQKQwMRERGJwtBAREREojA0EBERkSgMDURERCQKQwMRERGJ8v+lvncprxVTPQAAAABJ\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa5cb3db1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(v_params.elbo_vals)\n",
"plt.ylabel('ELBO')\n",
"plt.xlabel('iteration')\n",
"sns.despine()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, mini-batch ADVI's running time is much lower. It also seems to converge faster.\n",
"\n",
"For fun, we can also look at the trace. The point is that we also get uncertainty of our Neural Network weights."
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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LguFFRzja1ewUx/v7MerHNNrVhVUs4ns+mRdcs3jMF45v3e9KbNiwmCp15ZXB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\nRPc730GXV+5Drq+O2Ljg3rXWYq1FX3K/j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hpRRjnpmSbirnt4fGMD1TkDZYLFshoqRoXA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eZAhfsbO9LifXg2eTAYyZ13b2geKhNBrnBFUlkbiJANrdNezJ+kgESeQpVYimi/EzYrbbO1d/\nNnM/1+J6K0EFsFOun0eumemkk5cewShXc6Lax5KllmG3WKOdupnHs0eMRaxnYgfCL7Qy40JE1fHj\nx3nGM54BhHDcVVddRb+//eT6LMtotVr0+31uuOGGpgT7Ocrogf1EO3ei67TOsjA4ZdnV2kErymhd\ncjFIyej++0nSIIx36CCq9vceOmt2n+v890NBKO3akW35nT17wzn/1j3HzohNDQ2PFB7/+MezZ8+e\ns2pDoh15HDHOyR+P8nrAonBSbkjXa+Xht3F1dfPBFGUMAo/0Eun1VnGPaXpN7VgX9TyKBENWDlBV\nRUfkU0FSR3BWq5Qq0pSxIjN9oionMXkYOdeh8IWToLVhdzc4iGUV9tuKLUYpnAxOjhzrQhGKViy3\nSjqpodJ64jA6O2NnzY6OZUdrkxQyAUQwcopR4cJIeSXIij7KGuIqJ6tGyDmxKBAy+B5xVCGEI4kc\nO9sVUtbJlV5zgRzhvCD2dk5Ujd278XXzzEQ2ZlSjt469rYL2+gF5HdpS0tDNH0SKkHhZ/xTSSSqU\nE8Gx9iFCKTekq3mEgnYk0M7SLY7jY8nAx5RxNJetJDbx6MtoPCA93642PXbYIyCm5/pCdYS9S8VE\nHA4rTVBhMyP6UmGlIlKedrTZpLmZAilCTRzyseDrZvPb7FkqaaeGzs7QB4VXdUrXfHQJBJVS5ElC\n1Y4mnw0GCoQBIZDO0ioHRLbamDpb+/TSeTJVIvEhust0V0KA9J7HVg+gnCUxw/r8BEGUmCHdpGLP\nUolCYsz6yOnmQiAxOYIKZcr6q5KsHBIbQ6soNt0GwsK+417o6z6yWTKxV5I4G38WIpZSGqQo6ebH\n0Qa8Decs2kSMbRxfmZfQ67oAVZ1qOEkJrT8rcs0SA6wTFLliqWNYH3T3ArwUE1Honaed2pm5Tp4s\nsUjh50TsLLMDUnOmz5gTjYZo6ScFaNJySFas0irWQiQe2Nkpa8k3Vu5BKO9dKkBUOG8p8sVVYlxI\naChNUx566KHJTfr1r3+dOD65SaEHDhzg+uuv5xWvjIZ5DAAAIABJREFUeAUvfOELF2FOwwKxRUFx\n+DBL/+OHJ+8VhcHKiouWzgdARhHp+ecxnBFVS7ILwAOrB8680Y8Q7q3XqDpvd2vL71x8fpdvAd+9\nfwV+9gwZ1tDwCOCVr3wlV155JU9+8pNRavoD/J73vOeU2+r3+7z5zW9mMBhQVRVvectbeMpTnrLt\ndlrX7o8APCTlkDJON3hEHsGyzvH9Cl+P+lZWBUdmxp9QgzVaAiBCU807PYSqZx6HUZKxJJMevBfo\nwZAWhh1+xMhqtOvTSjXHZYw2IZVMDAsgnbRo0oSkN0QgWIo9RakQ3lPGijLSxGUwrvSCCEi1ZQWH\nNArhJbvp4+IlYuEx1uOdnBvZ72SWtSFYJ+fmYyhn6FQDVrMWSEiKkFa1vEfSzzTHBpI9YkBZLBH3\nSo7mbXZ1+0Fs4kPxCRzVukhgaSyxVkSmwqgIKWBP0icS8fSauCjM1XAOhCETBq8jhqWmnTh2WsPd\nowihgcrUYReN8BZ7V47uRug4m1Q+zFoO7xznuQO0K8/5OwuMAe9iVnsQtcGWCjBBVDmHk9AfTIub\naFshgQv9Q6yqCL3L0heSNRvjkVihEFisX3d+U0u/0CAEuzoVozLM/ern4T0pHC0GlFmX3jAhrYa0\nZJ9BOp53IxnKmFjBXCSg7pZKemLlGZgQZRo72EJYuuVxBnIHeZTiKlhOS1p11ETLMLhQ5BBnIbKT\nJY4qUpRa49xmVRg9yS5JPoooDMSxJRTxGBe+COlpWTVEejBSj2sm0B2t0MvCWmZZMeAx8SpCFaz6\n9uSya+kxtbLoJQm9NKMsFGZYsmdvzv6jLZb1Kk+I7uNQejkGBWhYy0F2ZsJKHoRjmMeTPi1q27Sv\nQpTJWbxUaGtCpGxGRDthUc5SCY0EOonFecE4tulZl8Ja77aMNS0cZiBBTiNo0huUzPH1fV1WHrIw\nyDEu/CHwGCnIhMc4gfDj+ZbTffiZKPM48DMVdwJZR51YMxwjY5AlCEL/aOdr5GmXJHIUlUAZi5F6\nErbxQlDFMeQW6wRKW9oabOKQrqBUEu8jnJBob2ipsKt+GZHmoKY3L9OJeRJpHfHqCn5vuPaRLVE+\niO7xJtH6+Yp4tLB0h0c4zD7EcEg8WtyyNQsRVW9961t57Wtfy3333cdLXvISVldX+aM/+qNttzty\n5AjXXXcdN910E0972tMWYUrDgskfOhgeZBddOHlvNCon86nGtC6+mGP/z+1kvg6P24ilpMP9qw+e\ncZsfKRwYr1G1Z+MaVWMuqysA3nugSf9raJjl3e9+N1deeeVC1kL88Ic/zM/93M9x7bXXcvfdd/Om\nN72JW2+9dfsNBSjhMGkL0Q/PPiFmnf2pM3VBdRCVRtyXh+hzsbuN0XIy2r4nLlg9XkASj5NpkHZI\nMjoKnI8XUCQZzpd4Cc4LtFc44VjKKtYOGWLjkNJN0o2E9Dghkd7QyVdZWUkR0YB2dZhSZPT8ErRL\nlgeO1Bj6LmLPcs4wTpCujg4AeZzRIozAz2b4LedDiqUuyll6VYwpJbrIabUGWBK0Ltm1ZNl/OJ2U\nkPYCuvkacWTw2S4S6dC9vD5TLZSXJKkisRbqFK9h3GYX5eR8LuVr5FphdQvroNIOUTrGtS1aZY+1\n1i7woKohUSrxKOLRiCqJKawmkpblVsGy9RQ6IlMOJT1dbUisp3JjISSR0oIPktY7Rzc1LLWDSPJK\n0o4rOj2HlxIhBVp4rHPggriwIiSkCQ9lP8EIxShu0YoHSBxLesjOwQqxifGqS6EUyoAmpnLT9KSq\n8qTVgMi1qFQcqi/WWBWiF3kRkuJKrUnq/ijrPhabgqizinLnY6XGRzHSapgUEphPWWynBldNe7FR\nCc5B5EsUdqIVChGDcpSJJa0K8AnCh+iAEBZEjvdZEEiurng4mxEGpElOoWKkFAwqTRKHeG/Y+QhB\nGKjXrsJ7xeyasZlyuAiGpUBXBpUwESlFpMkiS6flOdgLsqWykoNFm4Nli+WqYjBIaWvYF5XMZktK\nCVnVgzT8Rp+X9flvv4zzjk5iGY5Fi/B0xIg1Ulb6ERcmPcJsSAFIbKInAyKjSqJ6A2x3VygOIhw7\nspJICAZVxHK3QMpx0pyvUw3FTGbdxgQz74JuGyYt1lYj1FKoLhnlmrUySBIvJe2WwfQlS1HByigN\n62eN0+ZkSFl2QpLakmRJ44/l+Nww7MYo57hg9BByGNGPuyHF0o+PanoePAJtDEpKsrbDGEjbkr5L\n8GWJcYK2nqYERrailPUQkRIs7zTIXFPmEo8Ep0Mk2huQEoHBeyhKPUkK7OSrCNnDkbGSp+yJ+ghg\n1NdkHUMnMQhXUtJCCEtHr6FdxFJ+hEG1kIS9CQsRVUePHuXTn/4099xzD9ZaLrvsspOKVL3//e9n\nbW2N973vffzxH/8xQgj+7M/+7KSjXA2nn/zBIIqyCy6YvFeWBhcZLll67OS99MLwuRwG5z8fVVyy\nfCH/eei75FVOGqU0zHN4JYiqy87rbvmd85ZSVKY5cKiP935DPn9Dw6OVOI4XVgHw1a9+9eR3xxhD\nkmw9z3GWQSZQkeGY2U171EOLCpFoShdTEdGOKzJl2Z0fqX2XqRMsxNSrTKo+O1WPVeMR0dTh9Fri\ndYWyBuciwIeJ8EIwHEVE7TBnoCw1kgECxezk+CqN8ZUni0riogDbQimNtAbpHQWSzMVh25USdoXo\nTgQhbdFDUuVI3UVgMIiQzyem83yiMsckKWWSIk1FspYzitsoaYl1hbGCzjL4QiBFSX8Us7qmuOCS\nHgJBou1ktkeVRcFhJjh56eoKeRpjTcxKr8OPXnQX+3u7EcCe7ojDVUQx0OhljxDjQvJ+rord0aqi\nXTqETEl7Pcy+3UinQRYk2hKZCis0qIRxQelW5PDeMxQpuamjJIASHis8gyxGDiBN3CQlzAuP0qEw\nhhSW3Goy4RFW4YERER1fUBaKrrAMPXgDy2qFlllBesna8RYiBuUTpFdoESHSoGqMEVgjkUcNSpm6\nRLzHzMyFycoBgyoC2rjIYhy0dcman0bFhIAdg4McXA7VfIWXCBmRJv8/e+8Ws8l11nv+1qlWHd/j\nd+7+ut12u23HTpwEJyQwO4MgF8DFCImgueAGccUlSBEImUtQiIgQEoIrgkRyhSaCiaJBQpyk0Wj2\nFodhm70NOZjEjvvc3+k91nGtNRf1drc7NknAJgT4/jdulaveWl/Vqqrnv57/838Cbvmw7qbIVigB\nnocyvPEwsFhKaALLRcBnfUrDB1i7hlg7xKqlrQuaOlBpwWjY4BFUjaYOObOmYl1KSAWdkuimZTyo\nibSnCQEVOmR4SO96Q8UWgUbQ9PVqmwfkvnBzOyo5LQ3hLRooeyXplCLgNxmaFtnWlF1PezokTki0\nFJyuEybxw8d0ng/RcoHsWgKSRZbQVRLV9Nk37wRdK0kWS1TRzxHvQdQeaSEI1bMd2WvrBAKzOMat\nOyjEg8UT10nkrRqxFT2oleykolGQdw+llFFXI53AS83GiH/zXumzTp0QSJdyv1bIb+6vbee0UUpE\nw0V9hq1bXDmknHvCdvrgWjrVy5UbEYMyqBSqVT8nnJIE2bds6M/sAY3bkLHWS6I3kHIpA5Hy7GU1\nizxmuQZzuux762UGZyX58W129hpeFROq1iAIuBgqb+iOayQeIQyBXtLYOAXS05ysQWi2fQ1ItHR4\nNA3QtjHBSAiO4AU+CLJ4he+AFkQQSNEiZMSW7lhh37I271+Kd4RU/dqv/Ro/8AM/wJNPPvnPOu7F\nF1/kxRdffCeGcI5/JZQ3e/lefNBnqrwP+BZc3HE4fJi9SjakSiz6Atxy3XLp4AIv3/0y1+e3uTp9\n7Ds78H8HOJv1kpcn97/RAvUhxnGEzg3VvZKzRc14cE5Oz3EOgO/7vu/jV3/1V/nIRz6CMQ8Dvw98\n4APf9LjPfe5z/N7v/d4j2z7xiU/w3HPPce/ePX7+53/+2/8uSYMKEtn1gUdTerwMzDJLZA151pC2\nnkFdIr3CCxiZitPWkhpBraFqFeNkRdysCdjNyn2gSAML6ymTAVYFyrUmNO2mhimgV2vO3AgZOqL1\nKTWOrtWEPtbuhycdw62a0WKOaEoIU1ppEN6TmTXzLqN1lgvZGXePtlBBIYNEEWiUIGlPWer0Qa0Y\nSLwQeOlRrgUCxfqMu+khsuvQXYOWkCjLrnmFMzHpx+Hhvl0FToOUSNkRrMetBCczw2TYEqQgOEcQ\nknh1F98MaG3UF+97AMFBcgfZ5nx1to3TfT2VZxPsBQHCEbmSrJrjVODVSY65qSg7i6VDhq6/Rr7P\nfLU3Viy3Chof9VkCcd+6HkRkCJ27X/GCEh428su2FnQrTZRKggAdgVEeERwiQFsKdOCBeUfdKZJO\nssOql9IJaJyknNUEEZg1gaxyRLbC0cvN+to1WM4EERIRFKtVgpeSpChJmjVFGtHgSd2KaLXEqiml\n8BuVlGc+84jpo4pUgSBtFhyT9QRGW2ov0FQIQJkGZyroYkzbAH3dbxCStYvBBabhjPJE4gJI19AU\ngvlas1X1RXlx7HFDz7xW1I3HiZpSbDHvRrRSsNWu0L7Eh75mzAsQwW/knZC0c+b0AX+kNmMQHmi4\n7zS3VdR0QSIeqL38pg3Bpi5OAEHgpGK5FkyLCkLN0ZlDChChf2+IoBF4It9nY/19Ve99iZ30dF5v\nDEjegABd5fENyKARQSE6iQ8Rg2LBrEk3YwmbzJMk6gLaS/AdrTJIoFwrZAfRaskwXjC3W9TGPOjR\nJJFErmGwPmPZDilNgRCBZWJJnHtoI7Hh/zJ4guht5avSoKqWOFoycDeRnURLjyYiYOg6iTaegGBe\nRwgtib2iWK1xVYlT95cqoLa93FA0NYTNPfN90+pTMrrSE8mOppWYqB+QokOo7hEZppKezvYj8Eai\nXNhIPQORcrS9CJLQWfxm/9g4GheBl6i2QXZrRKJIpGcnX6PUinurjIUab+6poWo1xjuyxT1Wg53N\nO1rjTYJQkmHcks87lP7WHhDfLt4RUnV4eMgv/uIv8vzzzxPHD4O+H/uxH3snfv4c/4Yo72eqNqTp\nQeNf1XHpDaQqvp/JOjsGMqqyeUC6vj67eU6q3gLrZYOKFHls/sl9xnGETjU1cP3u8pxUneMcG/z9\n3/89AC+//PKDbUIIPvOZz3zT4z72sY/xsY997E3bv/SlL/Hxj3+cX/iFX+CFF174tsagHGTNHFrL\n7uo6GME9sj5AilqE6lf1pZfI0BCcIgxSxl6zCpI4dsRxIO0c8n4te4DRxHOSHqBWa7yXdLGBNcSi\nYykdAkW0XtPaESKALBtEZ2mV5WwFZtAhQ0tcrrgbrpBXryJ0R6Q7cu3o6o7Y1ORize3lkLunm4A1\nSAQB3yikDxA55CrgOnBolK8fZhA2/5WArmt8YwmtIyBRQrNMLMKD9gqNoaHur4MPRG7dx8YduCDA\nCzwC6QWqcQgcnXRINjbILeBBdhoTSiJRUS9yomG5CR7DI+MSoiZp19wMQ5RvuDPeZXCn2sgiBdJ1\nxG5JXp3SdBp7cko5HPS/EvrgvmclG3PnsMkzhIAI4n4igPjOKW5rylpF+NohbQl46jRFnAgetGEO\nAekVCkXQff2KDP2qufewzhWR62tWTKiQXc1S9hkq4RSqsujIocoG7zU+t5j6hKURKCsZBc98FtGc\nauREMBm03PCWoVzSdpL4aEYqdJ/g8QFCoJPJ/em2GaXABEmFBOGIxYq8WhOaiHRz/5fVkLYziK6l\nVjuUMkIta4SNNnq7ltMip5gbXBQQoe31nj6AdDQy4DYMWYYONrVEMvR9jsSGgMYBYtcAKeBQXdPn\nRVzb3wvREPmAFCmj9gzhHbGu0Romso9R+hogTZA9QSbAuJrh1IKjMEEF0d9nD8J7TNNQLiXroXkw\nu7tO0QnBdFDReYicRqGQSITTaC+IFg19CZREeIVoPYES51QviwvQVYo6TQnrBiMTvFizXEXYIrBc\nRgyOjii9xawqoqIhWEUZAlvlAm0ivNToLgAG07WEconOwOWKWmq24znLLmemY4IXVB1shZus/AE+\nOLraEIcON065YRVPrWZY1RGHjnIxJtkOBNnSqA7tLJ3TSFq6jXFGo/uMrNM5rW5RXUckOxye6fyI\nVRj0Sy4iYr1WZMsGoRQy7zO+RX3C6XJzE1xv3e9ExCzPGfs7wBDtOhoVYVrJyaKfD4XQaFOjZN0b\ngUhLTcxpnjM98wjt6YDYVdioo8saXl8r8DEmeFYmR8wcetmihwEbB4a3j1A5rNIM3woiFtwXH78T\neFuk6s6dO+zu7jIe98zwpZdeeuT/n5Oqf/+obt4CKYn3dgGoqz4VbawkjR661iX7m/qq4zvA46xX\nDVc3NVc35udmFd+IpnM0ZUcx+uYkaWA1ZuOCdP3ugndf/bd1OzvHOb5b8NnPfvYd+61XXnmFn/3Z\nn+U3fuM3eOqpp77t40b1bUw6RsmOW1tbHJ4tiL1kFfSbyAcBltqivCVsQrPZ0uIixXgj+ZlySpRv\nIa2lU5AZR+s8mZyRKMnQSpadp+/ZArHscB5kiBBSs1Q51ig0c5TokEHg74FOFEE5dtIld4Tj5txj\nY0GWdygdaFqJUj2rEwIS4ZC+Y3LaMmsaIrdEeI3KJdYppFZAS+clqyjBCAe+zyY1TlMHTSJHrJVF\na6CVtNJQS4UPiiaRiNiSsaQ6qxAi3tQcSUQIqOqMk0mGXcaUUQQVRNL1xfMeFqcaj0a0iqDqDSXY\nXO+NNMwTEM6xFzRfkQlWQexa4tUKkwliV2K6krkYE9wb/dZ6+zXlW6QKtNpgXcPY1veVfn2tjpU4\nG5Fs3Np8F1DW0RqF171piV1XrJICs6zwbU7SrjfB5xxVpyirka6iVRItAl7DbDxgNyk5dg8DPekD\n6WzJgL5GrtWWZLqkbMekSIx0HFUZqSsBQSwUe6M54SzQNYp2qVh1EfkIQgg0SU3vxPEQXnsiWvK0\nhWl/7aTztMEgG8/NekBUWKTzuNMWl2isELQyUMmOplPo6pRORayjbSJxP1QNSAR+Y7keJHgZcMKT\nCoELCisdwStsu2App+wWDbIUFOUMEZZU1QqqmMi3qACOgKZhd/k6QUqUtEgcbTRC+xMyWfayTSFR\nQmLdjGQlyLMVK9Vt5gkYuclYCUmkPa3QrGVfP+U7ifMSJx2T8i5LvYWkl6b2FXItYNCifqjqFX0t\nlAuKqg6s4xQhOoyDVho6KyFo7rgY2WiqmWLUzZGde5ClW8UJbRyxquFi6chNQ2kMg/WCSmpuLVOy\nHWh0S9ydkfo5seqo14I4EdzN9hme3WWxXjCM/oHF8hrCe2rXz7EQDMJpJqak8YauLZFSojsP0YZF\niX6xRABOtxsJZoz2HY1qCB1o34HQvYPfJosqFewsTtCtQqIwssEIjxQlwrd9aksGQhyhOk3WWupZ\nwr5+nXvtLmkcAQa/aok7QeI9zaTvEdcKSZ41xIuaUyyeDkEDIqA2WcXXzAGEsOmhBUZvykI3z2xi\nA2ld0aq+ifo8ylmoHB3W3/Y7/1vhbZGqn/mZn+EP//AP+cQnPsHv/u7v8tM//dPv1LjO8V2C8tYt\n7NYWciOvOZr1NVNZ+igZiKZThDGEuzdB9KTqwgNSdW6r/o342tESAgwG37x2QwrBdJxwxkNji3Oc\n4xy9y+ynP/1p1us1IQS899y8eZM///M//2f/1q//+q/TNA2/8iu/QgiBwWDAb/3Wb31bx4ogMcLT\nKMMyLtCp6le/1yUM+1yHxNMYxbyMyQe9e56Uga3TY2azGHYFUjgi0WCjrjeD8AGrA7frBNuV6Dph\nENXsFEtsELTHCq09TRqQJy1ju+REDJFe0VmFdrYPjBFIbxAYumFLmEmi0xQ76ZCZQcqAchKhPFK0\neA82cngRIFHIpq+/2qwzI4PG+74v1fK0RVxMSes11knkvLe7C0KhsSinaQl0ro9uuiBxQtMlEd0w\nIe4aVPBo6SmimjWghUB3MUatqa1FApmBHT9HhxqBwztBqSURK5RXNK0kdZJQRyxrQZIPCBtZ2L1Z\nTJ30JLfzknhREumEYtzhjjVGe2r30Bb8gcMdQOdxyoDrA/BeAClwSIJQJDYgfC+dkgLW84Db6t3J\nvFK0a1i+UlNnCQqP9b2nnJeCaHVMsZjTaIkzijSU+DawUBGpXcJqI+PqPLmU7NBh8ZSberZYQNsk\nfVcm6cl0RG0KIt+PMwktr+UDVAdba08bBGczRU1KNo1YG0/kI3IpUGGFaDTT4xuU2RShdE/UN652\nPgS8VMhlTbTqMGJN7DyBFJcsCV2Mahsi5akJ0EEjFc5LBsfXGawnnE17gxYZJF4Elq3mQlJhur6G\nCulZrRzxoDdnyGRA2yUrKjoihG+odASnvSOjHxruuwOus5wTsUfnI2ItcZ3EOcn9cjApHYk7RciN\nrXbos5taho3TnaDKx6SzNbZOEGHNbD1B0Bs5LONALQW2lgxsQ9X15F7dr/G6b3MvBY1R+FawnBtE\nCuKN3YABLT2VNbgoYtBVqI0Zh+gcRqSkWjEHTJcR2ggdWva4xzoYKhRCaY5LC1VDrCoK3TGfKVyn\n0EjWZUzlDEe7I/Z0Q7HoKNG4RlCVnsrpXuIrBNprQi1J2j4DKnEEU/XE0W3q2R4IfwPDbElDTUN/\nL53RnMwKVKuJBpIoCT1b7WkWIYjeRr01jJu7rNptWgK7zBClpopHxOWayB6zq2Y0QRPfi7he55gQ\nMVCOs/k9usEYmwt27Bm3vSZfDqijmOWOYno820g1Ja2wdFL12XslGSwqovkJYuPUqeqOsG5oWs2d\n1QAnY1rtiFz2bX4pvjXelu1FeEMx6Be+8IW3PZhzfHehW69pT88eSP8Avn6vlwMOi0cnoZCSeHeX\n6tYt0jRitagpbM7A5txcnDcA/kbc71E1Hf7TParuY3+rv9bX771ztp/nOMe/d/zSL/0SH/3oR3HO\n8ZM/+ZNcvnyZj370o/+i3/rt3/5t/uzP/ozPfOYzfPazn/32CZU3aNSD4otqPEAoiZQter1m0ehN\nvNV/1GMTsL5GRA5lO6x0JD6gtELKNYhApytIHamv0QJ0mzNvC4hyktiTdxaFJHECEzqMDaSDJUnq\nGViHFIKyi1BaIoMgVoHVUjM/MRu/BYl2mu445qSOsLlDDApS0xPTeXBMmjnT+hhtWiLtEFISbZZg\nN4I4XCeQHs5aTSRKRkd3IXKsplOEkkRNTS48AzSxkJR1wrq2m56bEo1CCIH1lqkoGQZJFGIkEisN\nU3qbZAnEKhDLCkmNkpu6m9AQz4+RIlA1W3THfSA90xk3lwmVl5yu7SONWoOA1klcleOqKyxXW0RI\nkIFSJXSRxncdQvRkJjT9wSLAzsl1IlESi8WDpqZ2c03kxgWtrAXdxi7cofF5hE8E2kCmW6SAhz5c\nAukVQUTEOkJujEtCUGTGUKQtwjscASnlIwYkAkhMg81aKm+pvUfHnsZuxit7U4T7DaQLVRGJBavM\nU3qDzXzffFlopAIdWqxwaO/Roo+mDQadOTJVoa0jUQHZdKimw0aAlwjlkDpgTcsTE/GgD5FYlIQA\nolwggydbl8TLJaLrf1tu3BBXq5hYOZyTNGtJZvreZ95LhJTkQjBRHtRDCwTfKdqZpur6CykEBGPQ\njUfVLVaBR9F14pHr5YIkBIGTNcvQ4ZMV2Jb7xuIuaNKgiHvnCGZOIptNz6lNLVUAitQxSh1KBYwN\nLHWGFp5ewOoJqvdazEKN1YJJsmYV3ui8IalsRas7bKgxobc4115yPySPfIfyHct5RN1qqpBDKghS\nkOoapTWnTcpZG3G3MrSNQgeH9P2clF5hTIQzGhU8CkHqmwdujQpJpBw2dhAknevt6YUrEcFhujnC\n3DcteRjnR6JBCYlpGsLGVbTVDcpLUisRoUXhUdIzrld9Ldi8puk0eenJmiWTeo1Skvu9qbxON3MC\nfGswSEatJPYarQJZnZGerZhWLVJq4lwQEoUxgigUNHZAtdLIeUdmJbqIWI8KdGZJ64plknISp9wV\nKcu5ZRbvIbYntCEhjQXLKGeVDHin8LZI1RudyN5IsM7xHwPl9RsAJIcXH2y7eXIEwHT45kmYHOzj\nVivSVLNa9i+jg2KXO6sjWvdWDQT/8+Lr9/rCyL3JP92j6j4OxilCCW4drf61h3WOc/y7QRzH/PiP\n/zgf/OAHGQwG/PIv/zJ/9Vd/9R0dQ0JNSoUSfUF5FtXEoiT1cyK7JLINUnbotCQqNJemgtwKcuOx\nZQudpXOKVZNRVSBFwLR99iiN19hEYiPNjt3Dmgi1CXZjv/m3hCLSRNKhZeBC0pLpXm6VR45paHmu\nu0d64hjXDbvjiCIRZFIjpUeyRKi6d8SSHlTASdjTMwpxRtm0uFIyzh3TaIWmxXYtkW+w5RotWk6F\n4/jMQoAsrohTi01gqCoEEqsdVgckkqTtUGWJ0jBMchAGIxS2k5jWs5OA0R2ZCKTSI4MgeIWwHXpy\nRqQblIRBWpMlNSmOWAcGGTCdUu5OkFrjvOSsVCgRMMIhhECKgBaQqN71TSuJSCWDqCUymnxxSjMr\nOZ45ksihgsM2LfEAhmKFkZ5ItQzcGkFAV0si4zh2EqccRnuk6ZAhYuU0RmqMgUGyQOKJTYuSAaN6\na2shA3krkfWQsSzYFgqNQ0owJqCFJ2iPUIE4UqRWkVmFjyOMlExEwlMTRRqvGLsj5KCjSlOqLMMm\ngknZMAgSHQxBGHZCg9Vjmp0JTatxnSBKWoL1RFqQRhKlegtrEyCWgZBLloVBjSSxCRgBceyxdoUI\nNYPQ4L1iklQMko7OaIISeKsxxyWxD+xGQx4bJUzLOVk5RylPoWoOEs3OsGOgzxAIMgnDVJGEDikF\nha3wSQwqJZES6yOMl4xVQmrpjULWnsR1JFRMrCfHM4g1SsJyYZg1fZ8qrXrjBi0lVgpsNmckJcNh\nST3ZwuUFw1GGFJJYK5SSaNExlAusWyNiRZoTbC88AAAgAElEQVR44iTgvMIjUCqwShNEviKWLbFa\n4yOPinzvRCkdRiuOGk0lBGa2QCwqWq8x1iF0hSBgpEAJiRABvTFkiHRHUq5oO8XJsmDR7KIs2Mwx\nGueMBhorIY09UvveaU9CIjsGvmKkWi62BYdqyiCR5KpjYB1p6sll/74ayoatsKIwNVY3JEkDzqHr\nGbEUjA8MInKgHFJ4DqdLyk7SBEksO7aPb5I2S4xt2BmumYQ1pl31zZlVw8VCcW01Y+I6rDPERFyI\nZ3zPgcbOAtU6MAkdSe6xXYTsal4/9azWHbkWHOSWJHHYSJKpNePsFCE9KRGJ9YzjFmtgOMhIupSJ\nSBjYmKQY0siYiCmR6uWJy6FmERStVpjpgKuHI545dKRRYKrnaCW+2Wv+n4V3xKgCHiVY5/iPgfL6\ndQCSN/SBuXtyBiTsT6Zv2j+5eAH+8q9IdOCobOk6x8Fgjy8e/SN3lkdcHO6/6Zj/rLh10hOki9v/\ndI+q+9jNelv1u6flua36Oc6xgbWWs7Mzrly5wksvvcSHP/xh1uvvrETWakGmIkaxZ6iX7KgRTw1a\nFmPHzdPADQFSdaSJxkwK8qrknrJ4UXAQDK+eVeTWclLGXFqNKbojOumYK42JBkgj2FUa1WjqRpBo\nR2o9iwbyyHMMaCWJAecCU9XQWoFViqm9xIXMUt+9xxeHEcOoxhQCc+qIpEFJidKBTtTsb13k5rRA\nzU6QouRw6yL3VseoMziSmiKOGciSNYHURnRuhWorTCsYRJqs07h6SRACowxBNOSxw/oj7ppdMpsw\ndp5qARO74uDS4ySmxOqKleqQ2rCVBPSlHdwtTdt1HBjLa6ohdB1KKq5kFyjbV0kyS5XtY+8Jcpni\ng2WflrupIUkiFo0mrGK8WBOLiFS3HCmPSHPyxhN3gXFuuTzN+GK7phqMCOuMiyzxdsk8FehI4TrD\n4eyYZefZKk+IjaZJUrTqKNYLgnNM4gG3TEwdapbrhGmiyAZjKjyVmWE6g0cwVhXSaqLSkBoog2Jv\n0jDpYhofIdhiGkuOlgsSY9jLdymN4cu3G+qVxOYJqlJEgJaKsem4lCaUVcb3qGNeNyVJalidCnIl\nmGQ5+/4ut1FUSJTuY7Q4T8HmuHVLG3KiwiM6hUAxTASTtG8Y29UjxsmCpXckOdTrQGQ7AppxsJQN\naBHYiSzltGBqlhSmRYoOdIKKLE20ZOpyxlnHe69dZP7l1zhThlFXMi4gi2Le9eRj3P3Kn6AbTaoU\nldxmsO54PINBHjgKESHfZ3brHmsJedBctA03lUEME/Qqg9BiizFFmeFaTxJpYg3HUlLEMeNkzTCt\nENKRKINEM1KGoZI8uSt5WRuabMxkWrBDAHmdVT0ndlB0klGWYoqIjILTtiIdpKxDg3QN1lakomZr\nviQ2vn/edUCqGuk0E6GpZYa2HVnZS18TLF45EneHabrNYGk5o0MbSZRasizj6X3D//Brjmee3eB4\nYmvCMkSs6zXxOMU3CcJX7E1HVPMFiVeYOKGIE/IiJTo7JhM167RAqZphrIl0YCwtT0tPoyrAs5MH\njkVglKQodQIipgsZgwRMJPBxw4Q5ewPFMDNUPmGYKkztcHVgWcVsbTm2GSHzPU6++jJSt1i5TZpm\nqG5BrFus1pzICKkqrowt4jiwXpSsJjtkcYJ3d2ipsLHmfeNd7mhHGwVcNCKEBSodMk49XiliYbkY\na6yzkFme2I3Y8gorIkbjlHunBhVf5JlBAK1Z3P468UAQWomQiiLOuHq4IvYJ+ybQ6YZqf8L/+X+8\nM9+Et0WqvvKVr/BDP/RDQG9acf/f9wO/P/uzP3v7IzzHvxlWr30dgOzypQfbTmdLNAkXtrfftP99\n8mVDX/C8WjQcFL3BxY3F7XNS9QYcnZYAPLH7rdPOe3mMijX1smS+ahjm314PnXOc4z8yfuqnfoqf\n+7mf4zd/8zf52Mc+xhe+8AWee+657+gYQpohR2OGhcJjKbbez545JbVHHI+XhDstopNoa5FRxIVn\nn+LslSMyf4Hntz3Wlvg84S6Wyf/8GiEdsdoa05iY5XSPa5MpX7sr2O4UurzLu689h1/fpm3O+OoR\nnCiFSlOm21Oa2RqrNVqlPL4b8cL73s/rf/MlANJpTH5pHw4DZn6CaTz7iefupQFuEaPHhzxzdcBf\nf/UvyV1HnG/hu5bBuw7Yn59wJCxWVzSm4MmRgm7F8YnC+YRpYhlGlsXiBCMtpdbkkwmjqcGdfZ1R\nPEDv7PHlWcOy9qgmwsYR8U6BchVxGujsmmRnyN40pbl1k6WMibdy4jvHdI1kNCxI3vO9+L/7LFms\naIsx3OtAa3SSku5uU0iPbzTuaI0TKamOcCaF7W0uDgraY0N2JpF1y8HuCCnXDKdXiK5eQH/lNQpK\nJrbkpemTtOkO4sYZ4xt3MCtDGnrbaCElJi6I4wLtDftX9njl1tcw3Qj1vS8wuVTgwoCyk3TVqzTz\nGVFtqTqJ2UvI2zlFGtOpFfLJHP03lk4MeeLikKGAJ8Yz9NMTxjuXGcWHvHzjb2njQLG3iyqXWAMT\nNGGaEMYp6Y2KwgrOigGlioliz4Wx5YVrI9zrJWnVUdYFojjFNQptNOlgi3x8gZNFi0k69LrDFAW7\nhxmD+T6rdItFMUGOK4yvoW3IqogyDAld4GCyQx7HHPiGG0vLbdURxSCmHepuh2o3C4VSESLF4HCX\naDxlpO4yTWIOkxEnTQVCIa1FX91luoLxwX/h1ukx7pVjIt8go4hkOqaSCauDSyy6NQeqYuc9TzJb\nn5IkCfJrOetyjZnuoE4ykkgi8udoVv8AeYcYDtjOO8axYjbtUPGa7b2ci/cE73r+CarmhAujbXy6\nx25i8XfvYGX/vO5cnKBPVkSy5UKSs6orIjlBJQnVssMrRZQ0pHLAfuFZmgqtLBcOcmx3xnRVM4oK\nrmeKidaok5Zm0bEzjXjX5ZivzxXX9t/LetFw8spr6JMVo4N9wvCAxx9vefn0dcT+hOFewnvf/zhf\n+rtXuWk08XBCVKdE1Zw8WpCkj6HtHCl61YsQAl0U2Ljk3Vcu8cpyzo2zhmc/tM9jY8fi1de4Vy9x\nWmKShGS6TTxUjE1Kt1IMjWCeFmTDAcPrZ0TJGRfzjnEeM378w5yUdzlqj1i3EjvZ4bHvTyhf0xRl\nSjk4xLR3yNWQ8buexZxBYnM6H9FmU7qTU9KLQxILp2cNbusiexcMR3/3RYw2DMyUeDJiOjHcvX2G\nB5JigBsnmGe3MfMV3SLBhoLxLtRFjKAlGg1J8iGTvS2mRcFjuebCNOEf/+s9ht0aN2mRdUwXEnIV\nkGLFU5em3CqmLJsV2Vn1jn0T3hap+uM//uN3ahzn+C7EekOq0kt9k8AQAqtlxRAYDN4sW7u/n66X\nQMpyUXHx3KziLTGb98Tzyjdp/Hsf+3mMSvri5Dsn63NSdY5zAD/yIz/CD//wDyOE4A/+4A949dVX\nefrpp7+jYzBpgckztktLGA941+Utnr/wFOum5Gt//ScYU2Gaht1Es7W1xTAdEFmLjneR3W0+/EPv\n45XrLfNyTbyzixQ168gjpGA8zBmOL1CwRN4uefziVS4+scvs7t+yOn0NuImQgkE64uK7cibzjht6\nyI2v3CPe2Wa4O+XsqWtkJnBWzxBaIWRHOhxjFws+8L7HuFEc8vr6pP9bVB8OKCGxckLwZwB875M7\n/L9zx+Dq0yxud6T6iK7IELrCTUccpjukPjA9vIbKhixUgbGGyCQkO1cYTrZZrkbI+RH51JLO4Mp4\ngotPEdqQxrC6NGHyvifYTVbczWPSmUPnBdMrNYvbS4Yj1bvVRTE6i5DjA8L4DFyfmZTCYrOYpy/u\n8OrpaxxVMyINlRBMJjmYiNYaYqVJUsHWkwe0qeHmqydctJYIR2wGDJKcUToCKZCyYTCO8Trm5OAC\nw9PXkXFMNBgSiRTlPR/50PPc+hOBcBEHhx1YyQv7z/DVsxXzV77OqZaUNQipkFKxNYnwrQQp8MOM\n1ePPsD5aoRRIYzHBYKxCasN4a5f3PL7LmY9IxgX5MqFdtSwr3RsjJCnhuae5MDnmMLb8X19echLN\nSMcjpBagNVvdiNom2DF8TRlilXJpcsBubrj5pZfZVqdMi0Az2ufSbsFV/xjPeYl+4iJ/e3QL0Upq\nqXA+pojH2C4QRYYf/dEf4uy//VduVzVbU8mFYW9fHrkCLybIyGKaAjv0jK5miBPIXvgQV5MBWdvS\nLW9Rzvvqk1YN6IxmHE2IRglHqcfQkE4zlqclPjpExCfIBeyOhrz7Azuc/MMKW2hOvgbYCEY5xg8Z\nBtidBho35F7Vz1+EQBvDanefXBwxvDLi/e+5iBIKXw+56GKsKcDDjN4capxomrhAO0GRjcj2pxyv\nloSdiARLNe9YNx4/UjwbSYZmyt12hmgERa7Ii4wiKti6dMi4OiZPDeu1IQ7wxEFgcrhD5HeZtGOE\nnNFMRlAr/PTRxWodK6JhipAKQkGFotgqiI8lPo5Q+RZd0yBl2ZtLxDFmGDO5uEe6OuLK+z9CFd1j\nvD7jymGNNoKD4VWCr9A2ZbUTcenSY8R+zrt2hnx/tsPffemEu04xKgYc8zV2/ZSJ7RDSE41GROMW\nebQAF4jNmI889jyvLI5Ylw57tkVdlwwGO0TDIen4KeTpy6RiSHHwLIsvfgkzsIh5A6IFIUiGI4rd\nKe2s49rO40w+9Az1F7+KqTzdCtRwgBtUwIb4aEOiB5i4X1wwrmJ84YNYNSeLdhlKR5TFpHvb7OzX\nrLJTJrsT5seSk1KTjkekBwW6SIlU72Si1Tsm2nt7pOrCG2Rh5/iPhRACq69+Dbuzjc77laeT8gyq\nfhIWwzdbgaeXDvtmb/NjelJVc+FyT6quz85t1e8jhMB62SC1pEijb7n/NImwmWEN3Dpace3S+F9/\nkOc4x3cx/uIv/oKrV69yeHjIn/7pn/K5z32OZ555hmvXriHl2yoV/udBKrLUUFzZo+zgma0+85xG\nCR+99mHuzP8GX3UkOiJNH0p9VZyw/f7/AsATeUNztqRJ34f2kuTOl7nVSi7Y3qDm8iDFbsophRBI\nqTeF3RopNFm+y3te6G3gb/7ff41OUoRWDEYJTzy9S1fUvPKXLyFthJAdz7xvh+/9gQ9hRyNu/N3D\nxa6DLObpy48xTp7FBsXFZo09fBwdbvPeoeD28ALh7j3W3SE7Tyq+Wh0xFDAZ7RIv1nRizuG7LnLr\nrsNPLLuDlsTGxElC6zWDvZz5usXqCKsiVukBNbeIBjGPjXZ4+okrrE7/J9JaDg5SntuOGOTP8te8\nzJ7IsJGiUyO8CxBNsSPPibHsTIcIIB7tIJVBmwSpBekg42B/SGUVwguslggBWkgGaUS6m3P3dI2W\nAk1ACI0UBVtbhtlp4HK+Jrl8EdYVmA5pIjIjiY0kFhJrDHEckepsE0n1hf1ZpHn3zpCvFymXcstL\n119HyQFnG7MDKSRdEveHbKTcvhhBdQcu7hMiQzG5ihCSYrTNYlaitWRSWFZdh6ghHip685OASvpv\n8SCLSOyj0vCAwBDw21PCaQ0yeuT5EEgem5Q8/4GnmRZDju78P2gJmVUkGtadZDuNWVe9af19Mw0A\naS1QE8eCyMALO5f5xy/d4V4b4Z0kiH67KDK2n/sAL5S9Nfe66qhf0XTNEqjoREwT+r/BqohL77vG\ns+/Z59VX/5ZqVpFFKYfbnjt1R7QJfg93BJUSvHa4jyuXTLTm8MIAEFhWBCU5GAqigwhRSowAp2LO\n4mv8b08+j5Sa/37r7xFCsp/HrJyibjbOgMDOUFBciFnf1eguQk+fYJwtKBd32U63yU9XPCPXzC4c\nstPeYl9FvHy7gQZ20hFR0pBFngtPXcCfjEHAP964RYsjH23hUkmsIoYuYftyzP/36l1EOmInS9ga\nxsApyEfDc0VKCB1Saa4dFBytIx7f3eJ28KzUCZnukBenRLHBFgMmlw5RG1cUoyT3b1124RLRl8cE\n35JtDVBKsHfwPKNRhtKWw4sFqxszUms355U0Ln9gLMHeBcLNUxZRQaQkWZSipKJIFR/4X15g3D7B\na/P+vEoVxHIfKRQCgYoTwPctevz9zJqmKyeslxUHj8XoJCZ/4nGq8S7jELh+74RW1oBgK8m5XcLW\nbsFgK+FW2xLv7JFMcsZxhLp5AiwfvCuff+Ei6+t3EHKfSjv+x60lOxe32L52CQjk3nFjfhuxqYl9\nJ/DO0bO3gZdeeolPfepT72jfkXO8PTTHJ7SzGZMPfe+Dba/PbmIaCxLStyADKo57CeDRTRgfslrU\nPJkdYlXE6+e9qh5gVrd0ZUcx/PYyTlIIdicpp5xy89ys4hz/yfHpT3+aP/qjP+KTn/wkX/ziF/n4\nxz/Oiy++yCuvvMInP/lJXnzxxe/YWAKCydDw2H5Pagb2YSPv/ekWo1FKyDq0qokmE0J488c7SSOe\nMUNuJBHpqqSbTSlUYC/f4alJTuMCd+/Vbzpue0dxs04opg8XWeIkR+kF2vQBS5pFcO0q7w5z7p3V\nrKM1WguSrb7f3bOPT7l3ewECpnHEtd2rABT7Y9LLl4HA6ddvsyMDt+kDhoBma2rZ37PUa42dTnj6\nPY9x/Ootdt91iSd3lvgQmEQNrqvQRvPkM7usvqZ47faCbtGTj2e2p9x8dYhznscv7WJjwwoQondT\nzLMBV9SUMpoQC/jQc/t8ieeRPnDl4DLH84p8/wJmkpEPY5qm6xv0So3Xuwy2JZcnlzku5zROcXL6\naL3d4xeGvH6nd1R9cqwossDdFUzGiv0ti5gHQtM7BsoNWdHA41s5t1tLEmmkEmgtSdIIKB+9r7p3\nc3v/dIu/mVuSaMx2ZjmZLx4Yqh0cjlj4AElK/J73wvoIpMLYt1YwGAWjocTZ+6TqDfNha597m3ky\n3LrK8voZ3hsi1VuPa/noN9v6jhA0l8aX2RqM3nQuLWEnecD7HoUQTD74AUbRdWS74CCXRFqTJ3Hf\n3DdoTkWEEY6nt58AIEv6Z0NKgZSGcR4DFcMoxfl+AeHJZ3bQpu+DNsoUWwPNsoPR9pQ7148Yxt9A\nGhPLcDTh2vQKHZuF3nn/jYwzxdbEYMuM4AQXhjH56KBflHgLaNWzDqv7c0RGEl2ImKYj9oqML58E\nnrI5rmkJWnOxKNCjHFcfkKxgb3rCWRPYyjPW0z2yccqFgyHXT0uMlhTbGXXVMRmkrHWCAC5cHmF1\nxHZ2g/WqwkpJpA3D7WcZDg2VOuK9778Mqw4jR2ixwsRDIgSHg5xnd7ZJ6yO+avqWAUIKtJGMB5bH\nLwwBuPrMDvOTgJIPJW4qjunWLUkc8ewIdqbjB7XaVw6GDMYJr5wsmKQeudRYrWltP38uX9piWT/L\n6rXTB/fUGEXbONIsZrB7jdGrJ8xOSpJE98/zBuljl5i+e4/29orSnPRNofsRPSD7Sgou7w84W9Y8\n9/gWTilYBh6f7GC6knJ+hrIGbTXWb1xV1cNzPHJPjUJs7D/jQvE931/wXx67tPlbBZGSXBkfcn11\n/S2P/5fg35xU/c7v/A6f//znybJ3zif+HG8fy6+8AkDx5NUH216f3cI0MXH+cKJ+I/KrT6D/8hUY\nw2rZIIXk4mCf12Y3cN6h5FtP/v9MeOXOguAD49G3tlO/j8f2BnyRG3z19uxfcWTnOMd3Pz7/+c/z\n+7//+yRJwqc+9Sl+8Ad/kJ/4iZ8ghMCP/uiPfkfHMmebxx77fobxm2sjhRDYNKFrPNPDK8jQYbMD\nbHr6pn0To7g6zrlb9oGPkhohBKO4D2TuvsW5p5cHHPptjH34GX/ue65xTIRQ5pF996YZWwPBf58p\nsjc0bR/mEdt7bw7ghRDoNKHbGH8oAe8aZoR0idq8++8nPLSWDMYZg/FVOn8/GyNQOsZ1FUr353v2\ncIL2UG6WzAfWoMXG5f0bzp0NL1GMD6luL0jf0Nn3qec++GC///0j38PtoxW3fS8joumwsaIYxMza\nId4UZEWKEJrjsgT+aROTIhK84TIipYDHDth3e8RffJVONAjVk1cjNVlsHox1/2JPSFoeva+j972X\n6vYdQgg8EwWWRQ5130pjnAzYmVxGnMoH31LxFhnWYpTArCRKHr2fgTe7LWtbcOUw54kskKUFjRwS\nmZLpYMDFvSk3Xr1JnjwkVpO6ZCuckuuHkrPk4IDy5k3seAt/liHbnqBMLRT7Q+a3H7b1EELwoXcf\nUDWOdrYhc5lkXXuGg4zQeX7if32WrfRRwhZHmu9//oBX/v4O89M5F7IpK/pxRVZjooc3YjpQLE96\nQnahUDw5eTRk3blYsJNPibVl2T3cHvj/2bvvOLnqevH/r1Onz87ubK/pBQIJhNBBFBALXokGRbx6\n9fLFL6Dfa6NZQL0WULkPH9cL6g9BL0SvQdpFUSxYEBJKCKSTnmyS7X13Zqef8/tjdidbZlu2zCZ5\nPx+PTXbPnDnnM2dO+bw/1UZRFfJKTBJHVFzuAM7S+cOO2UCapnB2qUnc0uivvy3zFVPlL8PUhxci\nO410oWhxQTUli+bh3taBJ5yeI0wpLIGAC6dDZ+XSEnRVob6uK50mt5k5E/u/R1MziSjHCk403STf\nFcDn8FHqLyISbsCla2iKC4/TwGFqdHTHcDl0vF4PKY+flNvP6YuKqK4IEMw/do07XQYEHPR2H0u7\nq7KCeFcHRiCAqirDBr/Kc+gYmsbZhR7yAinCZ55BpxLDUHXmlPgxgfUDCnjnLCikrSVEsG/grYrq\nfIKFHtTeLnrqj21XQUE1DMqrAhSX+YhGkoR6ohTOCzIvniKa76E4342qKly8PN0S7pzTStHVMlLR\nBmKpKMvmBFHcQQ5GopTrTs4o8uMyxs5XrqpY3jfK4vQO9JXzoKqmpoYHHniA22+/PddJEQP07N0L\npIOkfoc76tETAfJKRw4GfIsW4NiwDYBwKH2TqA5UsL+jlvqeJqryyqcx1SeG3fXptt5lwfEXJCwp\ny+MPChxpDk1XsoQ4ISiKgsuVvge9+uqrXH/99ZnlM21ewRzyXHkjvj43UEUkGaWkZE5mmWEmR1x/\nLEM/49BPrKoqqjY8A+gJzCEabuJtxcvQBgRcYzWVVPubD/n9qA6dikIvplOnxO+iOdiJO1DK0uqC\nzPq6qlLsduAzddxOP4bDh+lKv27oKsvmF7K961jmcUnRAsKO4bVwSl/gpQwJ4AZyGBo1ZX6aGzqw\nbJsFBV4qvC6iTREautPBaX7QTW8oTqlh0qlrKKaDYEUei5eVDNtef4Gf3l/wV5TPgpoz0fcdJYaO\nx5GkxOca93lm+HwYPh+KoqDU15NXVUhDLIG/uxMqA+iqTgpwmFrfZx6+jeIyP22qjeHU0QqLofsg\nli8fiGIrTlDcGA4dhzsI7RaqquA0j22oME/DDrrwuTxUFfuIJ4/VbimAY0hI610wH8/cOSiaxpLq\n8zjUuo9412HyS4IUm0Vs7Yn1fR/pfRi6hqFrtPeV9Rm6Qk2JSWEwnwU1+VRXDK8Bg2O1Qk53EN0M\nY1rDR8F1+ytp7zmUCcpdhoKmKngDc6DjCLbpY1Egn6C7AMv2EQr11cQ4+mqs3E5URWFxTT4KsC/7\n1zSIoSkMnPxlfkHN8JX6viiHZnJe5QqM/utJUWHAfFb9vC6DRDJFXr6LRDxFWWUeLe0aSSuFrowe\nDOgDCqE9psppRQbVi4rRNYVkysLQ06/HStLpXHF66bjOT1XXMQN5I66rqypnlwZo8RZg2/mUBudS\nF2+nui//5nOblAQ9eJzpEMLh1CmvOvZdq6qC2+sgOspgrLqu4fVpeH0OWvYpuJ06RSXezLnVz9tX\noBDu+3pNXSU/383BSBRVUXAbo4cxZ5cvI55KNzueCTkPqq688krq6upynQwxRGjP3nQTjAE1VUdb\nm3GRT7Bg5MEVvIsWYabSzSDCfTfgmkC6xKG286gEVcCBhnSR0fzy8U84N6/Ai+bSaWnrlWHVxSlN\n0zS6u7vp7e3lrbfe4qKLLgKgrq4OXc/5I22Qcp8Xj5E9Y5lV33Vdo6ZYUXLsffMWFRKNJtPzCAFO\nbxH0JnE4ho/Cmo2mO/DkVQ9frioE85y0dUUJ5rlwWSmS1rEsoarrBC84H0XXwYZk0iK/wI3p0Lls\n/rnDtgcwN3CssMjhLhz2emmFH60vM2ioOrqayhpQKAoEizy05GkUFBjDVxjCqWt4TB3T6GtGpB2L\nxPJ0jQKXg2RpOfmLSgbVhmTSqplU+Evxlyzhrdb9meWLy8roicRxh3rJ9CvqP0TjuA33ByqdnVFU\nfz6BM85BKTrWl21uuZ/lC4voSDQNPwaqgtGXcdULizGcedhtvTh9BilDR1cUfAX9BZ/tI6ZhYDI1\nPX1cDCP73KJKX1OqoDufYPUq2nsXoigKVtykqCqAlbIGHVsAX8F8ErFuFCVdk+UwtTH7C6f7Bxq4\nfOXE4r39CzOvOz1F5Jd4qQu1DXqf4fCDvxoSUUzNpNxXQmvvscDcyM8nuXAuaOm5MtW+bS4vyh5E\nqIpCudeJ29DTTReBAleAkuJFWdO9qCgPzAUE8rzo2tjnZT/TTAcebo/JSucZxFOJzAAJc0u8dJha\n9qaWA/gdKkb/99d3DWnjmGOpPzAd1KxU1cAGTR/ePz6zv9NPI9HRicvnZwED8isKFPhGft9EeRcu\nILR3H2bh+O5noyl2Oyl2H+ta4TZcuI3xtwqarNn1BBKzgp1K0bN3H67KCvS+ZpmWbdHS2kU14B+l\n2ZpnTg0OLV1aE+oLqubmp0cFPNhxhItrsj+ITyV1zekHz+lV4x9wosrvwvAYRFsidIXiBHwyAqA4\nNX3qU5/immuuIZlMsmbNGoqLi/n973/PD37wAz796U/nOnmDzM8fex66bHQFHAMyrm6vA/eAUT8N\n00fBqrM4VD9yRnq8ls0vJGXZ6VoAhmcSVaO/JB5KysZfEDSSwnGMeNpP01TKyid2r1uxqJj61jA+\nt4E9IG64/JK5HDzQRvWcghHfW7LoNJAaO7MAACAASURBVJJDSrQrAkUQAFdzul+wu7iEioiBI0uN\n4EiUvgmHYXgzPwUlk/Efjc/vJBZJUl7iJZRIoWkqBUMGjHJ6ijGcMTRj5Enl3V4HZaVOwkfGV2Na\n0Nd8ry0eQdVUVG14taHh8KeDHQ4A6f5vYxX85QfdNDf04M9zkpfvIhyKYQxpxjUwMHMbIx+noMsk\nlrIIxZNU+FwcTAYgnA7GXL5yrFQMpz5yrVBV32jG8eVnouzVKD/9DEzX4HN9Qb6XUDxJodsB7uJR\nP9tQhq6R73eQ3xeIGJpxrIYLCHgceE0Dp8ugrLKvL1RVgGTKyrq9gSqLfXgdBmX5I+fLDIcXf3DR\noABKVTR8hYvRjZGDI0cwiCM4fE7SqeYqK8NVNjVT7vgcOhW+mQuihpo1QZVtZy81ETOv92gdVjSK\nb9GxkprmcBtE06eLP8vIf/1Uw8A3bw5GLEqorwnGnEA6qDrQcXgaU31isGybtrZ0qdyCEZpGZKOr\nKoUFbo62RNhb18mqJcObrwhxKnjXu97FWWedRUdHR2YIdY/Hw7e+9S3OO++8Md6de+ctK8WyZtfz\nThuhj+xMc3nLSOnjL/0HqPa7ONTVS7Cvv5DLoVOYNzxT5c9zsfysylG35a6uojs2ehNrd00NvgPp\n1gbKeKqqxinbGTFwWUmZH3+eE5cn/TkTSStTa9FPM914A30BTf9wb0M68SuKQqDAjapM7Bz09+23\nOksfvONRXOYnv9CTCaR8/uH5CtPQuPSsinRN2ZmlMEI+UVGUETPSLu/4n5VmIEDRqouyvhZ0mZlz\nbCR5vnT63M7hWeszF4xdC+PymHj6CkwrisZXIGPoKgv6CjtGC2R181gNsidQQzIewjBHDr7F8Zk1\nQZU0Z5o9enanJ4z0LV6YWXa4sw4jnr7p5Y1SIpJ+3yLMNyKEutLNAF2Gk3JfCQc6DmPZ1qBhWU81\n9T0RYt0JPD4Tl2Nil9+CijyO7m5j04FWCarEKa2kpISSkmPXwNve9rYp2e7+/fv58Ic/zIYNGzDN\n6WmD78zS9Gwi8oqWDhpR62Ti8pVia+kalPHmCUo86eY+2dZ39vXH8PinsGZfUZi3qJBIJJFpSpde\nPnW76Ofq277P0FH6+qn0M8fonJ+/8mzyttYSMt3D1z2OtBr6sQBnqgytmcqmf3/qgKa9i4Jz2dt2\niOq82TOtj6roFAfjnFNWwI66iRUMjG1qTy6HqwCHa+Qa27EM7fc0HheeObmuH2pfzZ6mp6+BpcGp\nCe6n2qzI3VZUVLBu3bpcJ0P06dm1B0gHR/0OdR7FiKWDqdGa/wH4Fi3EkYoQi1skEumOsPMLaogk\nojT0ZBvH6tTx5uF27KRF1XE0o1k5L90/YdeR4aOHCSEmJxQK8b3vfQ+HY3Y3rdV0ZyaDkc38yjzK\nCk/c0XTHM3ffUCNl9N0ek/lLiqiZN3oTJtfS0wmsWJ71tf4+KwMzS26vIzPS2XRyGzpnFPlZfBwZ\nSN3t4oyVC6kq8TG3PG9QvtxtuCg6/QzynXnoeSMPtDLUbCn89jm8nF2+DNcoTdfSZi69DncQ0+kn\nLzh6bejx0D3pGiUjMIH+mdPI43VQWOpl3uLRa980Z/r70dxuDF0dVrM6EU5PMS5vGd7AXCA9eujA\nKSxmi1lTUyVmj55du9BcLtxVVZllhzqOYPYFVfkFo1cZ+xYvxky+BkCoO0Z+0M3C4FxerH2N3a0H\nqPCXTl/iZ7k397UAcPoo7fpHcv78IhRVob5JRgAUYqrdfffdfOELX+CWW24Z93uC/qltu58XcKJp\nCkUl48sszAt4SA1pSlhZPDtLcMfrrMVFDG0dqYwwt9BIKou9mVH1XKMEaYaukkhaOPIDGP7sz7Xz\nTi8lFk+xZ9vkyqAHxiMry89AU1Rebmvue00ZsN7gQGCs0c1GYxpaZr6isqCH+tYwFcXpYHDx4rNp\n909t0OHya8RC1qwJvmaSomqYrgIM3aA06MbvmbrCGcPvJ7BiRSa4mg1Ky8cOxg2/n7wzlqF7J18A\noSgqLt/oeUePoRFOpHBOInibLAmqxCCJ7m4idfUEVizPjAIE6f5QRfHlOJx6pk33SBxFhbj7Rhbq\n7uwlP+hmSWF6FMFdLft4x7wLp+8DzHIHj6THnj3/OJrvOU0df76TrvYIzd0Riqc4QyfEqeCJJ57g\nkUceGbSsvLyc9773vSxevHhC/XvnV05+4IaBDIeD+YtcjLeEvcg9u2vVjoeiKAwc0Cy/5MwRZqAd\n2fzK8ZXor1hUREtnhKLROvn3DRvu8hhEwgn0ETJscwKVBLzjuyf317B43Qah3kQ6ABw+svyUcjsN\nFlQGBjU7N5x5meHrp0Je2cwMWz0VSn1F7GsLU+wZPkLlZC2uOf6mdSMx/CMXlgSLvUR641O+z6lg\n5o9/QK7JWhL0E02mJlUQMVkSVIlBunfsBNJDafZr7+2kvbeL8qibYIVnXKVQgdIAdEHr/npq5hdS\nHSjHa3rY1rzrlB0SvDeRpKM5jKarLBjnQ3+ouVUBNrdF+OuOeq67YPTJDIUQw61Zs4Y1a9YMWnbV\nVVfxxBNP8Pjjj9Pa2soNN9zA2rVrx9zWVN/HVFXHF1yIpp18wVI24wlflWmcMN7tNKgpHV+tYGGx\nF9seuT9Jqa84M6fOeK1YVEw8kcIxjr5F4zWRM9KXP2/K9gvpZv6z4dle6iumOdzGnMDITfFKvUUU\nugsGzQU1GVV5ZfTEwmOvmIU/4KK9JYzHe3xBaf+Igac6XVXwTrLP6qTTkNO9i1mna9t2YHBQtbNl\nb7rpn6VQOM6mJcXzK+CNOE17DsM7z0RVVM4oWcLLRzZR19NIpX9qhs+c7eLJOJ2xHrqjPbxyqA5c\nh8mvMvjdnueJp+LEUwlSVgoLG9u20RQVVdUwNQO34cSlO/E7feQ5fOS78jh3aSGbNzfw+lvNElQJ\nMUX++Mc/Zn5/xzvewc9+9rOcpcUwp7+vzmzRP1CBPoVBxWT5TA8FrrysNRjZ4oWyQg8NrWFc5uif\nweh73RwwMpymKhMesGgkiwt8dMcSOEYYOnzZ/CBHm0IEx+gTPRllvokNNT5d/A4vF9esGnO9qQqo\nAGpGCeDGUlaRR37QPWpTVXFikKBKDNLx5hZUpxPfomMj/21p3Ikjkn7QF5aM74FfcfZSeGMLrUda\nMstWlp/By0c28drRzVSedmIHVZZl0RnrpiPSRXukM12bF+mkPdJBW29H399dRKIWdsKBnTQhaaL6\nnHT1Gvz37/aApff9aNi2mh6e11aPPbmVLlBAUW1QbBTFAtXCVWbR0NrEp763Ba+VImDbFKlQoeoU\nO0zyvAZenwfd40b3etG9HnSfDyPPj5GXhzbLO+ILkUuKosgUHzOktMKPpqkUjfO5MhMUReG0ESZ+\nzWZRdT4LqwJj1tB4vA5q5gdxebLXZk32nAs4DQLOkWvKgnkuglmGmhe5p6iKBFQnCQmqREakvp5o\nfT0F563KTPiYSCV4vX4rBck5QLoJxHiULKwAezMdIYtkKIzu9XB2+TI0VePlw5v4wGnvnq6PMSV6\n4xEaQy00hZpp6DxKXedRGrtbaeuNEo4Y2BE3WsyLknBD0oVlmaRSGkkrn2SigFQSUonpy5hFgO7R\nVlBAN2LoRgyH1oxLSeBLhsmL9pAXDZGfiFOoWwR8bpz5eZjBQlzFQTylJfirSnEV5qNqs6f0WIiZ\n8pe//CXXSThl6Lp2UjRdGm+TN98oczwG3fk0hloo886O2h4hxMRJUCUyWl/aAEDBeedmlr1Uu5Fw\nvJczlGpCQNE4J/7TdY2AG3rsAM0v/IPy974br+nhrLJlvF63hYMdR5ibXzX2hqaYbdtYySixeIj6\nzhb2tB5mT0sdDR0N9LalSPa6ScU8WJaHlOUkYZkkUiqJZDXJRBX22BOco+igmSpOt4JugmGCadiY\npo1p2Bi6jaml0DULXbUxlBS6aqGRQldsVDuFigW2hWLb2JaCBaRshWRKJWGrJC2NeEojlur7P5n+\niSdU4gmFRFwhlbCIRS2iKY0uNBpxAkEwSP8AxEBtVTC6wagLY+r7ceh7cWlJnEocTyJOXjJFsa5R\n4PdRWJRPYXUZwfmVePJ9s6L9vBBCnOjyXXmcV7kCY5Th8oUQs5sEVQIA27Jo/svfUE2T4PnnARBJ\nRHl8x+/QVR2924PpiJMfHP/8J5ULS9i+tZndv/0rpVdejmqaXD7vIl6v28Jze//GLed+fMrSb1lJ\nErFuYtEuOkMtHGipZ+fBBloaQ6R6kuiWQUp1E1M9RHHQa5lEUxqxuEIsXkQqPsoIQAqopoLpUXGY\nNk4zhctM4tYTuNQkTiWBw0pgWkmUZJJkHKJJg0jKIJowSMRMwimN3oRG3DApy/ficBiYhoauq5im\nhqHr6LrW96OiqAqgYAMpyyKVsklaFvF4knBPiB276zGTcSoD4In34I1GMJJxnHYSp2Lh0JLoJig+\nk5jDSa/DTVhzEVZMei2dSFIjllCJxRXiMYjHLWK9/TVrKmD2/RyjtimY9WEcb+3FaezCrSfxqHF8\nSpQ8O06hoRDwBymqqKZ66QIKSgpQtVkxFZ4QQkyKZ84cos3NqM6x5kY6fhJQCXFiy2lQZds2X//6\n19m9ezemafLtb3+bqqqZr70Q0PKPl4g2NlJ8xeXoHg+2bfPT1/+H1t523lv2LmpfibBgafGEZtKe\nu6SM7Vubaep1sPe/HmDhZ/8fZ5WdTrmvhBcPvcrViy6nOjDyjOixRIyuSDudoWbqmps5uK+VloZO\n4p0RDCuFqavYpknScBDXHMRUk4ilE7V0IgmNaLyKeBwSUQtrpKZ4io3m0HAFwOm0cZspPEYCtxbH\nrSRwWnG0VJJEQsO2HeiGG38gSFF5GaWlBfg9Jm6ngcuh43LoOB062pBjtHlvC3f9ZAO61+A/P/82\nqgOTm5jTtm0+++uNHHytgcrCQv79pgvHrDGKxGO0dLTQXFdH3eFa6mv3Ew61okTiOAHTMEj6vEQd\nfnp1H2HVRS8mkVRfABZXSMRJ13yFoQsN0AAHcKz2UneomIdacG9qwm0m8RgJPHocLzHcdhwjmUBN\nKWi6D28gSGlZBZXVZZSUBXG4HVLzJYSYldzVVbirJX8ihBhZToOq559/nng8zrp169iyZQv33HMP\nP/rRj3KZpFNStLmZQz/7OYphUPWhD2JZFmu3PMVLhzeysGAuyTcLgE5WXTRn1O3Ytk08aRGLp4jG\nk+gFBt1ajG1li2l8awt//OZ/kiqvxNtehtnr45Ftv8apgaErqKaObajENZO4ohNVTGJ2OkCKWSrx\npEo86SWR8JFMpPsrWUlrlDF5bSCFooLhUHB4FBxmCpeRwqUmcJHEnUoQBAodJtWlJVSeNp+i+ZXo\njqnrMLplfyv//rNXQYFVF1ZPOqCCdPv9959bw4/2d7BtXyvr/rSb6965eNSAxGU6qC6ppLqkknPO\nPi/rOrZt0xXroTnUSmu4nYMtRzjYVEt7ZyvRcC9qzMJI6jjIAztAAh9x20k0ZRJNasQS6Vqv3i6L\n3i5I3150YEDnaBU0U0MzFcxuMBsbce6ow6mlcGhJnEoSB0kcVhzDSmIkEpBIYiUVUujYmhPD5ced\nV0BeYRH5wQA+rwNXX2DrdGi4zHSA6zA1CdKEEEIIMSNyGlRt2rSJSy65BIDly5ezffv2XCZnVrJt\nG8vu+9+ysfr/t2xSlk0qZZFMpUgkbCLxOJF4nHg8QW9vlGg0RjjcSyweJRaJEk/GSETiJBJxUtEY\niXgcO54klUxizzsL22nw50eexrLTA9CdpqxAOaxQr+xCKYPHnvsNyh+UdOswRQUFLFUBRcVSNFKK\nSro3kEpSUUnZGsm5BhHbpLXqMpKWQrJXIWn4SHoglVBIJW2siIXdbWGnRhvYwaY/glINBV0H3Qm6\nbmOoFqaWwmUn8Fkx8pIJSlSoynNTOreSwJwqAjXluHzTP/KRZdlEYkka28I8/uJ+1m86CjYsO6+C\nz79j6ZTt59LqIp4/p4ydLxzmf/60m39srefKVdVcuqKCYJ7zuIIJRVEIOP0EnH4WFc7jwppzsq4X\nSUTpiHTS1ttOa08TraFmOsLtNIU7aA130xWLEY/4UCIB1JgPLeHGSpokUzqJpEoyYRHvsYkP+roH\n1nwNTRgomoqqg6YraBEbvasXve4QmmqjqzaaaqGpNpqS/lEZ/KPYNgo2at//WOn/FQvsvuXYSt8c\naoAFqqag2CqKqqJrKqqhYeo6hq5jOExMh4HTYeJwOvG4HTjdHtx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f/vKXnHPOOblORkZP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snGfWvv4u9e+ze+f+gF/vqaT8xKuxYzo729nV/84he8+OKL1NTUcP/9959zWy+99BKCIPCD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\nbDabzWaz2Ww2m+0E/P9AQ44jxm4GXQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa5db76e0b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace);"
]
},
{
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"metadata": {},
"source": [
"## Summary\n",
"\n",
"Hopefully this blog post demonstrated a very powerful new inference algorithm available in [PyMC3](http://pymc-devs.github.io/pymc3/): [ADVI](http://pymc-devs.github.io/pymc3/api.html#advi). I also think bridging the gap between Probabilistic Programming and Deep Learning can open up many new avenues for innovation in this space, as discussed above. Specifically, a hierarchical neural network sounds pretty bad-ass. These are really exciting times.\n",
"\n",
"## Next steps\n",
"\n",
"[`Theano`](http://deeplearning.net/software/theano/), which is used by `PyMC3` as its computational backend, was mainly developed for estimating neural networks and there are great libraries like [`Lasagne`](https://github.com/Lasagne/Lasagne) that build on top of `Theano` to make construction of the most common neural network architectures easy. Ideally, we wouldn't have to build the models by hand as I did above, but use the convenient syntax of `Lasagne` to construct the architecture, define our priors, and run ADVI. \n",
"\n",
"While we haven't successfully run `PyMC3` on the GPU yet, it should be fairly straight forward (this is what `Theano` does after all) and further reduce the running time significantly. If you know some `Theano`, this would be a great area for contributions!\n",
"\n",
"You might also argue that the above network isn't really deep, but note that we could easily extend it to have more layers, including convolutional ones to train on more challenging data sets.\n",
"\n",
"I also presented some of this work at PyData London, view the video below:\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/LlzVlqVzeD8\" frameborder=\"0\" allowfullscreen></iframe>\n",
"\n",
"Finally, you can download this NB [here](https://github.com/twiecki/WhileMyMCMCGentlySamples/blob/master/content/downloads/notebooks/bayesian_neural_network.ipynb). Leave a comment below, and [follow me on twitter](https://twitter.com/twiecki).\n",
"\n",
"## Acknowledgements\n",
"\n",
"[Taku Yoshioka](https://github.com/taku-y) did a lot of work on ADVI in PyMC3, including the mini-batch implementation as well as the sampling from the variational posterior. I'd also like to the thank the Stan guys (specifically Alp Kucukelbir and Daniel Lee) for deriving ADVI and teaching us about it. Thanks also to Chris Fonnesbeck, Andrew Campbell, Taku Yoshioka, and Peadar Coyle for useful comments on an earlier draft."
]
}
],
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gwern commented Jun 8, 2016

< 40 seconds on my older laptop. That's pretty good considering that NUTS is having a really hard time. Further below we make this even faster. To make it really fly, we probably want to run the Neural Network on the GPU.

This comparison would make more sense if you had given timings for NUTS on this problem. I have no way of knowing if 40s is very good or mediocre.

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LeZhengThu commented Jun 11, 2016

Is this Python 3? I'm using Python 2.7 and get some errors.

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