Variational Inference for De Finetti Logic

We introduce De Finetti Logic, a novel formalization of the data model of Gamma Probabilistic Databases. De Finetti Logic is a simple, database-centric probabilistic programming framework in which models are specified through relational constraints applied to a probabilistic database. This framework is grounded in the concept of Polya urns and offers an intuitive formalization of exchangeability, the fundamental structural assumption underlying Gamma Probabilistic Databases. We leverage this new formalism to develop a novel inference mechanism based on variational methods. Starting from a DFL theory, our inference method automatically identifies an appropriate family of variational distributions to approximate the target posterior, and synthesizes an optimization algorithm to minimize the Kullback-Leibler divergence between the true posterior and its variational surrogate. To maximize performance, we employ knowledge compilation techniques to limit the number of variational parameters, while preserving the expressive power of the surrogate. Our method is implemented as an extension to the StarfishDB system. Experimental results demonstrate that (i) our approach provides a practical, scalable, and fast-converging alternative to general-purpose inference via collapsed Gibbs sampling, and (ii) remains competitive with specialized algorithms that leverage model-specific optimizations.