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guest_blog_post.ipynb
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guest_blog_post.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.stats as stats\n",
"import pymc3 as pm\n",
"import arviz as az"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"az.style.use('arviz-white')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Probabilistic Programming\n",
"\n",
"This post is based on an excerpt from the second chapter of the book that I have slightly adapted so it's easier to read without having read the first chapter. \n",
"\n",
"\n",
"## Bayesian Inference\n",
"\n",
"Bayesian statistics is conceptually very simple; we have _the knowns_ and _the unknowns_; we use Bayes' theorem to condition the latter on the former. If we are lucky, this process will reduce the uncertainty about _the unknowns_.\n",
"\n",
"Generally, we refer to _the knowns_ as **data** and treat it like a constant, and __the unknowns__ as **parameters** and treat them as probability distributions. In more formal terms, we assign probability distributions to unknown quantities. Then, we use Bayes' theorem to combine the prior probability distribution and the data to get the posterior distribution.\n",
"\n",
"\n",
"$$p(\\theta \\mid y) = \\frac{p(y \\mid \\theta) p(\\theta)}{p(y)}$$\n",
"\n",
"Here $\\theta$ represents the parameters in our model, generally this are the quantities we want to learn, $y$ represents the data.\n",
"\n",
"Each term in the Bayes Theorem has it's own name:\n",
"\n",
"* $p(\\theta \\mid y)$: posterior\n",
"* $p(y \\mid \\theta)$: likelihood\n",
"* $p(\\theta)$: prior\n",
"* $p(y)$: marginal likelihood\n",
"\n",
"The prior distribution should reflect what we know about the value of the parameter before seeing the data $y$. If we know nothing, like Jon Snow, we could use _flat_ priors that do not convey too much information. In general, we can do better than flat priors.\n",
"\n",
"The likelihood is how we introduce data in our analysis. It is an expression of the plausibility of the data given the parameters.\n",
"\n",
"The posterior distribution is the result of the Bayesian analysis and reflects all that we know about a problem (given our data and model). The posterior is a probability distribution for the parameters in our model and not a single value. Conceptually, we can think of the posterior as the updated prior in the light of (new) data. In fact, the posterior from one analysis can be used as the prior for a new analysis.\n",
"\n",
"The last term is the marginal likelihood, also known as evidence. For the moment we will think of it as a simple normalization factor. \n",
"\n",
"\n",
"## Probabilistic Programming: Inference-Button\n",
"\n",
"Although conceptually simple, fully probabilistic models often lead to analytically intractable expressions. For many years, this was a real problem and was probably one of the main issues that hindered the wide adoption of Bayesian methods. The arrival of the computational era and the development of numerical methods that, at least in principle, can be used to solve any inference problem, has dramatically transformed the Bayesian data analysis practice. We can think of these numerical methods as universal inference engines, or as Thomas Wiecki, a core developer of PyMC3, likes to call it, the inference-button. The possibility of automating the inference process has led to the development of **probabilistic programming languages (PPL)**, which allow for a clear separation between model creation and inference.\n",
"\n",
"In the PPL framework, users specify a full probabilistic model by writing a few lines of code, and then inference follows automatically. It is expected that probabilistic programming will have a major impact on data science and other disciplines by enabling practitioners to build complex probabilistic models in a less time-consuming and less error-prone way. \n",
"\n",
"I think one good analogy for the impact that programming languages can have on scientific computing is the introduction of the Fortran programming language more than six decades ago. While Fortran has lost its shine nowadays, at one time, it was considered to be very revolutionary. For the first time, scientists moved away from computational details and began focusing on building numerical methods, models, and simulations in a more natural way. In a similar fashion, we now have PPL, which hides details on how probabilities are manipulated and how the inference is performed from users, allowing users to focus on model specification and the analysis of the results.\n",
"\n",
"In this post, you will learn how to use PyMC3 to define and solve a simple model. We will treat the inference-button as a black box that gives us proper **samples** from the posterior distribution. The methods we will be using are stochastic, and so the samples will vary every time we run them. However, if the inference process works as expected, the samples will be representative of the posterior distribution and thus we will obtain the same conclusion from any of those samples. The details of what happens under the hood when we push the inference-button and how to check if the samples are indeed trustworthy is explained in Chapter 8, _Inference Engines_.\n",
"\n",
"\n",
"## PyMC3 primer\n",
"\n",
"PyMC3 is a Python library for probabilistic programming. The latest version at the moment of writing is 3.6. PyMC3 provides a very simple and intuitive syntax that is easy to read and close to the syntax used in statistical literature to describe probabilistic models. PyMC3's base code is written using Python, and the computationally demanding parts are written using NumPy and Theano.\n",
"\n",
"**Theano** is a Python library that was originally developed for deep learning and allows us to define, optimize, and evaluate mathematical expressions involving multidimensional arrays efficiently. The main reason PyMC3 uses Theano is because some of the sampling methods, such as NUTS, need gradients to be computed, and Theano knows how to compute gradients using what is known as automatic differentiation. Also, Theano compiles Python code to C code, and hence PyMC3 is really fast. This is all the information about Theano we need to have to use PyMC3. If you still want to learn more about it, start reading the official Theano tutorial at http://deeplearning.net/software/theano/tutorial/index.html#tutorial.\n",
"\n",
"\n",
"> Note: You may have heard that Theano is no longer developed, but that's no reason to worry. PyMC devs will take over Theano maintenance, ensuring that Theano will keep serving PyMC3 for several years to come. At the same time, PyMC devs are moving quickly to create the successor to PyMC3. This will probably be based on TensorFlow as a backend, although other options are being analyzed as well. You can read more about this at this [blog post](https://medium.com/@pymc_devs/theano-tensorflow-and-the-future-of-pymc-6c9987bb19d5).\n",
"\n",
"\n",
"### The coin-flipping problem\n",
"\n",
"The coin-flipping problem, or the beta-binomial model if you want to sound fancy at parties, is a classical problem in statistics and goes like this: we toss a coin a number of times and record how many heads and tails we get. Based on this data, we try to answer questions such as, is the coin fair? Or, more generally, how biased is the coin?\n",
"\n",
"While this problem may sound dull, we should not underestimate it. The coin-flipping problem is a great example to learn the basics of Bayesian statistics because it is a simple model that we can solve and compute with ease. Besides, many real problems consist of binary, mutually-exclusive outcomes such as 0 or 1, positive or negative, odds or evens, spam or ham, hotdog or not hotdog, cat or dog, safe or unsafe, and healthy or unhealthy. Thus, even when we are talking about coins, this model applies to any of those problems.\n",
"\n",
"In order to estimate the bias of a coin, and in general to answer any questions in a Bayesian\n",
"setting, we will need data and a probabilistic model. We are going to generate the data using Python, but you can also generate the data yourself using a real coin!"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(123)\n",
"trials = 4\n",
"theta_real = 0.35 # unknown value in a real experiment\n",
"data = stats.bernoulli.rvs(p=theta_real, size=trials)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model specification\n",
"\n",
"Now that we have the data, we need to specify the model. This is done by specifying the likelihood and the prior using probability distributions. For the likelihood, we will use the binomial distribution with parameters $n=1$, and $p=\\theta$ and for the prior, a beta distribution with parameters $\\alpha=\\beta=1$:\n",
"\n",
"We can write the model using the following mathematical notation:\n",
"\n",
"$$\n",
"\\theta \\sim \\mathop{Beta}(\\alpha, \\beta) \\\\\n",
"y \\sim \\mathop{Bern}(n=1, p=\\theta)\n",
"$$\n",
"\n",
"A justification of this model is discussed in chapter 1. But briefly we can justify it as follows. Coins can take only two values heads and tails, thus we can use a Bernoulli distribution with n=1, as this distributions models the distribution of two mutually exclusive outcomes like heads (1) or tails (0). We use a beta distribution with parameters $\\alpha=\\beta=1$ as this is equivalent to a uniform distribution in the interval [0, 1]. That is we are totally ignorant of the value $\\theta$ can take, besides being some number between 0 and 1. If instead you have reasons to think the value should be around 0.5, you could use a beta distribution with parameters $\\alpha=\\beta=2$ or $\\alpha=\\beta=20$, I suggest once you have read this post you try using those priors and see how the inference change.\n",
"\n",
"This statistical model has an almost one-to-one translation to PyMC3:"
]
},
{
"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 (2 chains in 2 jobs)\n",
"NUTS: [θ]\n",
"Sampling 2 chains: 100%|██████████| 3000/3000 [00:00<00:00, 3017.95draws/s]\n"
]
}
],
"source": [
"with pm.Model() as our_first_model:\n",
" θ = pm.Beta('θ', alpha=1., beta=1.)\n",
" y = pm.Bernoulli('y', p=θ, observed=data)\n",
" trace = pm.sample(1000, random_seed=123)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* The first line of the code creates a container for our model. Everything inside the `with-block` will be automatically added to `our_first_model`. You can think of this as syntactic sugar to ease model specification as we do not need to manually assign variables to the model.\n",
"\n",
"\n",
"* The second line specifies the prior. As you can see, the syntax follows the mathematical notation closely. \n",
"\n",
"> Please note that we’ve used the name `θ` twice, first as a Python variable and then as the first argument of the Beta function; using the same name is a good practice to avoid confusion. The `θ` variable is a random variable; it is not a number, but an object representing a probability distribution from which we can compute random numbers and probability densities.\n",
"\n",
"* The third line specifies the likelihood. The syntax is almost the same as for the prior, except that we pass the data using the `observed` argument. This is the way we tell PyMC3 we want to condition the unknowns ($\\theta$) on the known (`data`). The observed values can be passed as a Python list, a tuple, a NumPy array, or a pandas DataFrame.\n",
"\n",
"Now, we are finished with the model's specification! Pretty neat, right?\n",
"\n",
"\n",
"### Pushing the inference button\n",
"\n",
"The last line is the inference button. We are asking for 1,000 samples from the posterior and will store them in the `trace` object. Behind this innocent line, PyMC3 has hundreds of _oompa loompas_, singing and baking a delicious Bayesian inference just for you! Well, not exactly, but PyMC3 is automating a lot of tasks. If you run the code, you will get a message like this:\n",
"\n",
" Auto-assigning NUTS sampler...\n",
" Initializing NUTS using jitter+adapt_diag...\n",
" Multiprocess sampling (2 chains in 2 jobs)\n",
" NUTS: [θ]\n",
" Sampling 2 chains: 100%|██████████| 3000/3000 [00:00<00:00, 3017.95draws/s]\n",
"\n",
"The first and second lines tell us that PyMC3 has automatically assigned the NUTS sampler (one inference engine that works very well for continuous variables), and has used a method to initialize that sampler.\n",
"\n",
"The third line says that PyMC3 will run two chains in parallel, so we can get two independent samples from the posterior for the price of one. The exact number of chains is computed taking into account the number of processors in your machine; you can change it using the `chains` argument for the `sample` function.\n",
"\n",
"The next line is telling us which variables are being sampled by which sampler. For this particular case, this line is not adding any new information because NUTS is used to sample the only variable we have `θ`. However, this is not always the case as PyMC3 can assign different samplers to different variables. This is done automatically by PyMC3 based on the properties of the variables, which ensures that the best possible sampler is used for each variable. Users can manually assign samplers using the step argument of the sample function. \n",
"\n",
"Finally, the last line is a progress bar, with several related metrics indicating how fast the sampler is working, including the number of iterations per second. If you run the code, you will see the progress-bar get updated really fast. Here, we are seeing the last stage when the sampler has finished its work. The numbers are 3000/3000, where the first number is the running sampler number (this starts at 1), and the last is the total number of samples. You will notice that we have asked for 1,000 samples, but PyMC3 is computing 3,000 samples. We have 500 samples per chain to auto-tune the sampling algorithm (NUTS, in this example). \n",
"These samples will be discarded by default. We also have 1,000 productive draws per-chain, thus a total of 3,000 samples are generated. The tuning phase helps PyMC3 provide a reliable sample from the posterior. We can change the number of tuning steps with the `tune` argument of the sample function.\n",
"\n",
"\n",
"\n",
"### Summarizing the posterior\n",
"\n",
"Generally, the first task we will perform after sampling from the posterior is check what the results look like. The `plot_trace` function is one of many ArviZ functions we can use for this task:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1200x200 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace(trace);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By using `az.plot_trace`, we get two subplots for each unobserved variable. The only unobserved variable in `our_first_model` is $\\theta$. Notice that $y$ is an observed variable representing the data; we do not need to sample that because we already know those values.\n",
"\n",
"In the above figure, we have two subplots. On the left, we have a Kernel Density Estimation (KDE) plot; this is like the smooth version of an histogram. On the right, we get the individual sampled values at each step during the sampling. From the trace plot, we can visually get the plausible values of the parameters according to the posterior distribution.\n",
"\n",
"Another plot we can make with ArviZ is a posterior plot."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_posterior(trace, round_to=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can interpret this result as follows, on average the value of $\\theta$ is 0.33, this means the coin is most likely biased towards tails, as we used 0 to represent tails and 1 to represents heads. This estimation is pretty close to the real value of $\\theta=0.35$, the value we used to generate the synthetic data. We can see that PyMC3 and our model has provided a reasonable answer. Of course for real examples we do not know the _true_ value of the parameters, that's the whole point of doing inferences in the first place.\n",
"\n",
"As we can see from this example we did not got a single number for $\\theta$ we got a distribution of plausible values. This distribution represents the uncertainty in our estimate. There are many ways to express the uncertainty of a Bayesian Analysis one is to use a **Highest Posterior Density** (HPD) Interval, as in the previous plot. For this particular example the hpd interval says that the 94% of the plausible values are contained within the 0.02-0.64 range.\n",
"\n",
"Getting the posterior is not the end on a Bayesian Analysis. As with other forms of modeling a Bayesian analysis is an iterative process and is motivated by a particular context and set of questions. But I hope this simple example has make you learn more about Bayesian Analysis"
]
}
],
"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": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}