{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Probabilistic Programming\n", "\n", "A Probabilistic Programming Language (PPL) is a computer language providing statistical modelling and inference functionalities, in order to reason about random variables, probability distributions and conditioning problems. The most popular PPLs are `Stan`, `PyMC`, `Pyro` and `Edward`. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A probabilistic program is a mix of **deterministic computation** and **sampling**, which allows to *draw random values* from distributions, to *condition* variables on observations and to perform *inference*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pyro\n", "Pyro is a universal probabilistic programming language based on Python.\n", "\n", "It can represent any probabilistic model, while providing automatic optimization-based inference that is flexible and scalable to large data sets. \n", "Pyro builds on PyTorch library, which supports GPU-accelerated tensor math and includes automatic differentiation, a technique for efficiently computing gradients.\n" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### Models\n", "The basic unit of probabilistic programs is the stochastic function (or model). A statistical model is a mathematical description of how the values of some knowns and unknowns could generate the observed data.\n", "\n", "![image.png](attachment:image.png)\n", "
S. Wood, \"Core Statistics\"
\n", "\n", "\n", "A stochastic function in Python is an arbitrary function that combines two ingredients:\n", "\n", "- deterministic Python code\n", "- primitive stochastic functions that call a random number generator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Using `sample()` primitive** \n", "\n", "Drawing a sample from the unit normal distribution $\\mathcal{N}(0,1)$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pytorch sample:\t tensor(0.6614)\n", "pyro sample:\t tensor(0.2669)\n" ] } ], "source": [ "import torch\n", "import pyro\n", "pyro.set_rng_seed(1) # for reproducibility\n", "\n", "loc = 0. # mean \n", "scale = 1. # standard deviation\n", "\n", "# using pytorch\n", "normal = torch.distributions.Normal(loc, scale) # create a normal distribution object\n", "x = normal.rsample() # draw a sample from N(0,1)\n", "print(\"pytorch sample:\\t\", x)\n", "\n", "# using pyro\n", "x = pyro.sample(\"sample_name\", pyro.distributions.Normal(loc, scale))\n", "\n", "print(\"pyro sample:\\t\", x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pyro samples are named: Pytorch backend uses these names to uniquely identify sample statements and change their behavior at runtime depending on how the enclosing stochastic function is being used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Drawing multiple samples**\n", "\n", "Now we draw multiple samples from $\\mathcal{N}(2,2)$ and $\\text{Exp}(0.3)$ distributions and plot the corresponding histograms." ] }, { "cell_type": "code", "execution_count": 2, "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", "import matplotlib.pyplot as plt\n", "import pyro.distributions as dist\n", "\n", "# distributions\n", "normal = dist.Normal(2, 2)\n", "exp = dist.Exponential(0.3)\n", "\n", "# multiple samples\n", "normal_samples = [pyro.sample(\"n\",normal) for i in range(200)]\n", "exp_samples = [pyro.sample(\"n\",exp) for i in range(200)]\n", "\n", "#plot\n", "fig, axes = plt.subplots(1, 2, figsize=(12,4))\n", "sns.distplot(normal_samples, ax=axes[0])\n", "sns.distplot(exp_samples, ax=axes[1])\n", "axes[0].set_title('Normal')\n", "axes[1].set_title('Exponential')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Seaborn `distplot()` automatically estimates the PDFs over histogram bins." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Simple stochastic model**\n", "\n", "Suppose we want to reason about how temperature interacts with sunny and cloudy weather. We can define a simple stochastic function `weather()` describing the interaction\n", "\n", "\n", "$$ \\mathcal{N}(12.0,5.0^2) \\; \\text{for cloudy weather}$$\n", " \n", "$$\\mathcal{N}(23.0,6.0^2) \\; \\text{for sunny weather} \\; $$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{'weather': 'cloudy', 'temp': 8.512848854064941},\n", " {'weather': 'cloudy', 'temp': 12.010722160339355},\n", " {'weather': 'sunny', 'temp': 19.3258056640625},\n", " {'weather': 'sunny', 'temp': 14.052600860595703},\n", " {'weather': 'sunny', 'temp': 32.76374816894531}]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def weather():\n", " # generate a binary sample\n", " is_cloudy = pyro.sample('cloudy', dist.Bernoulli(0.3))\n", " \n", " # convert binary sample into categorical\n", " is_cloudy = 'cloudy' if is_cloudy.item() == 1.0 else 'sunny'\n", " \n", " loc_temp = {'cloudy': 12.0, 'sunny': 23.0}[is_cloudy]\n", " scale_temp = {'cloudy': 5.0, 'sunny': 6.0}[is_cloudy]\n", " temp = pyro.sample('temp', dist.Normal(loc_temp, scale_temp))\n", " \n", " return {\"weather\":is_cloudy, \"temp\":temp.item()}\n", "\n", "[weather() for _ in range(5)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could use this stochastic function to model the sales of ice cream based on the weather." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[tensor(31.2418),\n", " tensor(36.3404),\n", " tensor(18.3335),\n", " tensor(23.0716),\n", " tensor(7.7725)]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def ice_cream_sales():\n", " is_cloudy, temp = weather()\n", " expected_sales = 200. if is_cloudy == 1 and temp > 35.0 else 20.\n", " sales = pyro.sample('ice_cream', pyro.distributions.Normal(expected_sales, 10.0))\n", " return sales\n", "\n", "[ice_cream_sales() for _ in range(5)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inference\n", "\n", "The purpose of statistical inference is that of using a statistical model to infer the values of the unknowns that are consistent with the observed data.\n", "\n", "\n", "|Frequentist interpretation|Bayesian interpretation|\n", "|:-:|:-:|\n", "|Probability measures a proportion of outcomes. | Probability measures the believability in an event. |\n", "|There is randomness in our estimation of the parameters, but not in the parameters themselves, which are considered as fixed.| Parameters are treated as random variables and our belief about these parameters is updated in the light of data.|\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian inference\n" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Bayes theorem**\n", "\n", "Let $A$ and $B$ be two events, such that $P(B)\\neq0$, then $\n", "P(A|B) = \\frac{P(A,B)}{P(B)}=\\frac{P(B|A)P(A)}{P(B)}$.\n", "\n", "\n", "
\n", "
https://medium.com/informatics-lab/probabilistic-programming-1535d7882dbe
\n", "\n", "**Bayes theorem example**\n", "\n", "There are two boxes $b_1$ and $b_2$. Box 1 contains three red and five white balls and box 2 contains two red and five white balls. A box $B\\in\\{b1,b2\\}$ is chosen at random with $P(B=b_1)=P(B=b_2)=0.5$ and a ball chosen at random from this box turns out to be red. \n", "What is the posterior probability that the red ball came from box 1?\n", "\n", "$R\\in\\{0,1\\}$ indicates whether the chosen ball is red or not.\n", "\n", "From Bayes theorem we get \n", "$$\n", "P(B=b_1|R=1)=\\frac{P(B=b_1,R=1)}{P(R=1)}.\n", "$$\n", "\n", "and $P(B=b_1,R=1) = P(R=1|B=b_1)P(B=b_1)=\\frac{3}{8}\\cdot \\frac{1}{2}$. \n", "\n", "From the law of total probability $P(R=1)=\\sum_{i\\in\\{1,2\\}}P(R=1|B=b_i)P(B=b_i)=\\frac{3}{8}\\cdot \\frac{1}{2}+\\frac{2}{7}\\cdot\\frac{1}{2}=\\frac{37}{112}$.\n", "\n", "Consequently, $$P(B=b_1|R=1)=\\frac{3}{16}\\cdot\\frac{112}{37}=\\frac{21}{37}\\approx 0.56$$" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Posterior probability**\n", "\n", "Under the Bayesian paradigm we do not estimate parameters, we\n", "compute their distribution based on the given data.\n", "\n", "The posterior probability is derived according to Bayes' theorem\n", "\n", "$$\n", "p(\\theta|x) = \\frac{p(x|\\theta)p(\\theta)}{p(x)}\n", "$$\n", "\n", "and the idea of uncertainty is preserved by the specific interpretation attributed to the involved terms:\n", "\n", "- **prior probability** $p(\\theta)$ = degree of belief of event occurring before observing any evidence\n", "- **evidence** $p(x)$ = observed data\n", "- **likelihood** $p(x|\\theta)$ = compatibility of the evidence with the given hypothesis\n", "- **posterior probability** $p(\\theta|x)$ = updated belief given the evidence\n", "\n", "
\n", "\n", "
https://www.researchgate.net/figure/Bayesian-updating-of-the-prior-distribution-to-posterior-distribution-The-Posterior_fig1_320507985
\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Conjugate priors\n", "\n", "If the posterior distribution $p(\\theta|x)$ belongs to the same family as the prior distribution $p(\\theta)$, then the prior is said to be a **conjugate prior** for the likelihood function $p(x|\\theta)$.\n", "This is a particularly convenient case in which the posterior distribution has a closed-form expression.\n", "\n", "These are just a few examples of conjugate priors:\n", "\n", "|Conjugate prior distribution| Likelihood | Prior hyperparameters | Posterior hyperparameters|\n", "|:------:|:-----:|:-----:|:------:|\n", "|Normal|Normal (known var.)|$$\\mu_0,\\sigma_0^2$$|$${\\frac{1}{\\frac{1}{\\sigma_0^2}+\\frac{n}{\\sigma^2}}\\Bigg(\\frac{\\mu_0}{\\sigma_0^2}+\\frac{\\sum_{i=1}^n x_i}{\\sigma^2}\\Bigg),\\Bigg(\\frac{1}{\\sigma_0^2}+\\frac{n}{\\sigma^2}\\Bigg)^{-1}}$$|\n", "|Inverse Gamma|Normal (known mean)|$$\\alpha,\\beta$$|$$\\alpha+\\frac{n}{2},\\beta+\\frac{\\sum_{i=1}^n (x_i-\\mu)^2}{2}$$|\n", "|Beta|Binomial|$$\\alpha,\\beta$$|$$\\alpha+\\sum_{i=1}^n x_i, n-\\sum_{i=1}^n x_i+\\beta$$|\n", "|Gamma|Poisson|$$k,\\theta$$|$$k+\\sum_{i=1}^n x_i,\\frac{\\theta}{n\\theta+1}$$|\n", "|Gamma|Exponential|$$\\alpha,\\beta$$|$$\\alpha+n,\\beta+\\sum_{i=1}^n x_i$$|" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Beta-Binomial case**\n", "\n", "$Beta(\\alpha,\\beta)$ prior and $x\\sim Bin(n,\\pi)$ likelihood result in the posterior\n", "\n", "\\begin{align}\n", "p(\\pi|x,\\alpha,\\beta)&\\propto \\pi^x (1-\\pi)^{n-x} \\pi^{\\alpha-1}(1-\\pi)^{\\beta-1}\\\\\n", " &\\propto \\pi^{x+\\alpha-1}(1-\\pi)^{n-x+\\beta-1}\n", "\\end{align}\n", "\n", "which is a $Beta(x+\\alpha, n-x+\\beta)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Approximate inference\n", "\n", "Prior $p(\\theta)$ and likelihood $p(x|\\theta)$ functions are usually known as part of the model, while the computation of the normalization factor \n", "\n", "$$\n", "p(x) = \\int_\\theta p(x|\\theta) p (\\theta) d \\theta\n", "$$\n", "\n", "can easily become intractable in the high-dimensional cases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Example of intractable posterior**\n", "\n", "Suppose we are trying to figure out how much something weighs, but the scale we’re using is unreliable and gives slightly different answers every time we weigh the same object. We could try to compensate for this variability by integrating the noisy measurement information with a guess based on some *prior knowledge* about the object.\n", "\n", "$$weight \\, | \\, guess \\sim \\mathcal{N}(guess, 1)$$\n", "\n", "$$ measurement \\, | \\, guess, weight \\sim \\mathcal{N}(weight, 0.75^2) $$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def scale(guess):\n", " weight = pyro.sample(\"weight\", dist.Normal(guess, 1.0))\n", " measurement = pyro.sample(\"measurement\", dist.Normal(weight, 0.75))\n", " return measurement" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model is quite simple, so we are able to determine our posterior distribution of interest analytically. But in general the exact computation of the posterior of an arbitrary stochastic function is intractable. \n", "\n", "Even the `scale` model with a non-linear function may become intractable." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def intractable_scale(guess):\n", " weight = pyro.sample(\"weight\", dist.Normal(guess, 1.0))\n", " measurement = pyro.sample(\"measurement\", \n", " dist.Normal(some_nonlinear_function(weight), 0.75))\n", " return measurement" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Approximate inference addresses the need of applying Bayesian learning to more complex problems and to the high-dimensional datasets that we are dealing with in machine learning.\n", "\n", "Examples of approximate inference include Variational Bayesian methods, Markov chain Monte Carlo, Markov Random Fields and Bayesian Networks.\n", "We can identify two main categories for approximate inference:\n", "- **Stochastic methods** turn the problem of inference into a problem of sampling from the posterior distribution of interest;\n", "- **Deterministic methods** substitute inference with optimization problems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "- S. Wood, \"Core Statistics\"\n", "- [Pyro library](https://pyro.ai/)\n", "- [Pyro documentation](https://docs.pyro.ai/en/1.1.0/index.html)\n", "- [Probabilistic Programming & Bayesian Methods for Hackers](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/)" ] } ], "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 2 }