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Probabilistic thinking is an incredibly valuable tool for decision making. From economists to poker players, people that can think in terms of probabilities tend to make better decisions when faced with uncertain situations. The fields of probabilities and game theory have been established for centuries and decades but are not experiencing a renaissance with the rapid evolution of artificial intelligence(AI). Can we incorporate probabilities as a first class citizen of software code? Welcome to the world of probabilistic programming languages(PPLs)

The use of statistics to overcome uncertainty is one of the pillars of a large segment of the machine learning market. Probabilistic reasoning has long been considered one of the foundations of inference algorithms and is represented is all major machine learning frameworks and platforms. Recently, probabilistic reasoning has seen major adoption within tech giants like Uber, Facebook or Microsoft helping to push the research and technological agenda in the space. Specifically, PPLs have become one of the most active areas of development in machine learning sparking the release of some new and exciting technologies.

Conceptually, probabilistic programming languages(PPLs) are domain-specific languages that describe probabilistic models and the mechanics to perform inference in those models. The magic of PPL relies on combining the inference capabilities of probabilistic methods with the representational power of programming languages.

In a PPL program, assumptions are encoded with prior distributions over the variables of the model. During execution, a PPL program will launch an inference procedure to automatically compute the posterior distributions of the parameters of the model based on observed data. In other words, inference adjusts the prior distribution using the observed data to give a more precise mode. The output of a PPL program is a probability distribution, which allows the programmer to explicitly visualize and manipulate the uncertainty associated with a result.

To illustrate the simplicity of PPLs, let’s use one of the most famous problems of modern statistics: a biased coin toss. The idea of this problem is to calculate the bias of a coin. Let’s assume that xi = 1 if the result of the i-th coin toss is head and xi = 0 if it is tail. Our context assumes that individual coin tosses are independent and identically distributed (IID) and that each toss follows a Bernoulli distribution with parameter θ: p(xi = 1 | θ) = θ and p(xi = 0 | θ) = 1 − θ. The latent (i.e., unobserved) variable θ is the bias of the coin. The task is to infer θ given the results of previously observed coin tosses, that is, p(θ | x1, x2, . . . , xN ).

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