sparta: Sparse Tables and their Algebra with a View Towards High Dimensional Graphical Models

A Bayesian network is a multivariate (potentially high dimensional) probabilistic model, which is often formed by combining lower dimensional components. Inference (computation of conditional probabilities) is based on message passing algorithms that utilize conditional independence structures. In Bayesian networks for discrete variables with finite state spaces, there is a fundamental problem in high dimensions: A discrete distribution is represented by a table of values, and in high dimensions such tables can become prohibitively large. In inference, such tables must be multiplied which can lead to even larger tables. The sparta package tries to meet this challenge by introducing new methods that efficiently handles multiplication and marginalization of sparse tables. The package was written in the R programming language and is freely available from the Comprehensive R Archive Network (CRAN). The companion package jti, also on CRAN, was developed to showcase the potential of sparta in connection to the Junction Tree Algorithm. We show that sparta outperforms existing methods for high-dimensional sparse probability tables. Furthermore, we demonstrate, that sparta can handle problems which are otherwise infeasible due to lack of computer memory.