Abstract
Probabilistic programming languages are used for developing statistical models. They typically consist of two components: a specification of a stochastic process (the prior) and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. In this article, we establish a probabilistic-programming extension of Datalog that, on the one hand, allows for defining a rich family of statistical models, and on the other hand retains the fundamental properties of declarativity. Our proposed extension provides mechanisms to include common numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program. Observations are naturally incorporated by means of integrity constraints over the extensional and intensional relations. The resulting semantics is robust under different chases and invariant to rewritings that preserve logical equivalence.
Highlights
Languages for specifying general statistical models are commonly used in the development of machine-learning and artificial intelligence algorithms for tasks that involve inference underACM Transactions on Database Systems, Vol 42, No 4, Article 22
An actively studied concept in that area is that of Probabilistic Programming (PP) (Goodman 2013), where the idea is that the programming language allows for specifying general random procedures while the system executes the program not in the standard programming sense, but rather by means of inference
DARPA initiated the project Probabilistic Programming for Advancing Machine Learning (PPAML), aimed at advancing PP systems, focusing on a specific collection of systems (Pfeffer 2009; Mansinghka et al 2014; Milch et al 2005), toward facilitating the development of algorithms and software that are based on machine learning
Summary
Languages for specifying general statistical models are commonly used in the development of machine-learning and artificial intelligence algorithms for tasks that involve inference underACM Transactions on Database Systems, Vol 42, No 4, Article 22. Languages for specifying general statistical models are commonly used in the development of machine-learning and artificial intelligence algorithms for tasks that involve inference under. The relevant inference tasks can be viewed as probability-aware aggregate operations over all possible outcomes of the program, referred to as possible worlds. Examples of such tasks include finding the most likely possible world or estimating the probability of a property of the outcome. DARPA initiated the project Probabilistic Programming for Advancing Machine Learning (PPAML), aimed at advancing PP systems, focusing on a specific collection of systems (Pfeffer 2009; Mansinghka et al 2014; Milch et al 2005), toward facilitating the development of algorithms and software that are based on machine learning
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