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Formalisms for specifying statistical models, such asprobabilistic-programming languages, typically consist of two components: aspecification of a stochastic process (the prior), and a specification ofobservations that restrict the probability space to a conditional subspace (theposterior). Use cases of such formalisms include the development of algorithmsin machine learning and artificial intelligence. We propose and investigate adeclarative framework for specifying statistical models on top of a database,through an appropriate extension of Datalog. By virtue of extending Datalog,our framework offers a natural integration with the database, and has a robustdeclarative semantics. Our Datalog extension provides convenient mechanisms toinclude numerical probability functions; in particular, conclusions of rulesmay contain values drawn from such functions. The semantics of a program is aprobability distribution over the possible outcomes of the input database withrespect to the program; these outcomes are minimal solutions with respect to arelated program with existentially quantified variables in conclusions.Observations are naturally incorporated by means of integrity constraints overthe extensional and intensional relations. We focus on programs that usediscrete numerical distributions, but even then the space of possible outcomesmay be uncountable (as a solution can be infinite). We define a probabilitymeasure over possible outcomes by applying the known concept of cylinder setsto a probabilistic chase procedure. We show that the resulting semantics isrobust under different chases. We also identify conditions guaranteeing thatall possible outcomes are finite (and then the probability space is discrete).We argue that the framework we propose retains the purely declarative nature ofDatalog, and allows for natural specifications of statistical models.

Declarative Statistical Modeling with Datalog