## Anglican - A Probabilistic Programming System

Anglican is a probabilistic programming language integrated with Clojure and ClojureScript.

While Anglican incorporates a sophisticated theoretical background that you are invited to explore, its value proposition is to allow intuitive modeling in a stochastic environment. It is not an academic exercise, but a practical everyday machine learning tool that makes probabilistic reasoning effective for you.

Do you interact with users or remote systems? Then you often make the unfortunate experience that they act unpredictably. Mathematically speaking you observe undeterministic or stochastic behaviour. Anglican allows you to express random variables capturing all this stochasticity for you and helps you to learn from data to execute informed decisions in your Clojure programs.

## Getting started

You can also clone the examples repository and run lein gorilla to get a quick setup.

A typical hello world example in statistics is a coin flip model. Our coin has two sides, head and tail. Intuitively given a set of observed values of a coin you would now like to know how fair it is. Mathematically speaking we want to know the probability of head turning up. Let’s encode a model for this:

(ns anglican.coin-flips
(:use [anglican core emit runtime]))

(defquery coin-model [coin-series]
(let [prob (sample (beta 1 1))] ;; 1. prior
(loop [[f & r :as s] coin-series]
(when (seq s)
(observe (flip prob) f) ;; 2. incorporate data
(recur r)))
prob))


Anglican provides us primitives to build a model for our coin. If you are familiar with Clojure, you will spot them: defquery, sample and observe. defquery just sets up the scope of our model and allows us to give it the name coin-model and define an input slot for our data as coin-series. In 1. we define our prior belief without seeing any data. Let’s just pick the beta distribution, because it defines a probability between 0 and 1 and we assume that the coin is rather fair. You can incorporate any other prior belief by tweaking the two parameters of the Beta distribution though.

(sample* (beta 1 1)) ;; => 0.7185479773538508


(Note: sample* has to be used if you run it outside a query.)

In our model we then sample this value in the query and will plug it into the flip distribution to observe each data point in 2.. If we have no data then the loop will not run and we will get just our prior belief samples. This is not really that helpful though. Anglican does its magic when you start to provide observed values from the coin. For this we use doquery.

(->> (doquery :smc coin-model [[true]] :number-of-particles 10000)
(take 10)
(map :result))

;; => (0.98529804829141 0.5948306954057996 0.5948306954057996 0.3579256597687244 0.9818148690925241 0.9818148690925241 0.4539746712124162 0.8944478678159888 0.8944478678159888 0.3433014675748332)


(Note: doquery receives a few arguments for the Sequential Monte Carlo method. You can look up each of those for inference. An attribute of the method is that you might get the same value multiple times in a statistically consistent manner.)

You might know from real-life or a statistics course that having very few examples, only one here, will not allow you to infer the probability of head. Anglican provides you a so called posterior distribution after seeing the values. As you can see our distribution is already considerably tilted towards 1.

Let’s assume we observe 8 times heads:

(->> (doquery :smc coin-model [[true true true true true true true true]] :number-of-particles 10000)
(take 10)
(map :result))

;; => (0.9068541546104443 0.9068541546104443 0.9664328786599636 0.9664328786599636 0.9664328786599636 0.9664328786599636 0.9664328786599636 0.9664328786599636 0.9664328786599636 0.9664328786599636)


Our posterior distribution confirms our intuition that this coin is very unlikely, but still incorporates some uncertainty about the actual flipping probability. We can be pretty sure that somebody is trying to cheat with this coin here… Congratulations! You have just conducted your first Bayesian inference. Bayesian inference allows you to both intuitively incorporate expert knowledge in the prior to work in a small data regime, while correcting wrong prior beliefs with more data.

What happens if you pick a different prior, e.g. tweaking the beta parameters to 10 and 10? Try to use a larger data set. Do you see that the effect of the prior belief vanishes?

## Theory

Anglican and Clojure share a common syntax, and can be invoked from each other. This allows Anglican programs to make use of a rich set of libraries written in both Clojure and Java. Conversely Anglican allows intuitive and compact specification of models for which inference may be performed as part of a larger Clojure project.

### Language

Anglican provides a language to abstract the statistical inference from the Clojure runtime. If you are just interested in using Anglican, you can read the details of it in the language section and ignore the details about inference. You might have to try to different inference methods depending on the nature of your model, but you do not need to learn any of the statistics involved.

### Inference

The underlying inference methods are document in the inference section. If you have a statistics background or are interested to learn more about the mechanics behind Anglican’s language primitives you are invited to study the details. If you have any particular questions feel free to join our slack channel.

### Background

The theoretical background is documented in peer-reviewed, state-of-the-art academic literature.

## Contributors

Core contributors, in order of joining:

as well as many others, in alphabetical order:

## Funding

This work is supported under DARPA PPAML through the U.S. AFRL under Cooperative Agreement number FA8750-14-2-0004. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation heron. The views and conclusions contained herein are those of the authors and should be not interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA, the U.S. Air Force Research Laboratory or the U.S. Government.