Constraint-Based Inference: A Bridge Between Constraint Processing and Probability Inference

Abstract

Constraint-Based Inference (CBI) [1] is an umbrella term for various superficially different problems including probabilistic inference, decision-making under uncertainty, constraint satisfaction, propositional satisfiability, decoding problems, and possibility inference. In this project we explicitly use the semiring concept to generalize various CBI problems into a single formal representation framework with a broader coverage of the problem space, based on the synthesis of existing generalized frameworks from both constraint processing and probability inference communities. Based on our generalized CBI framework, extensive comparative studies of exact and approximate inference approaches are commenced. First, we extend generalized arc consistency to probability inference based on a weaker condition [2]. All the existing arc consistency enforcing algorithms can be generalized and migrated to handle other concrete CBI problems that satisfy this condition. Second, based on our CBI framework we apply junction tree algorithms in probability inferences to solve soft CSPs [1]. We show that the message-passing schemes of junction tree algorithms can be modified to achieve better computational efficiency if the semiring of a CBI problem has additional properties. Third, we study loopy message propagation in probability inference for general CBI problems. We claim in [1] that for CBI problems with a idempotent combination operator, the loopy message propagation is an exact inference approach. Our experimental results also show that the loopy message propagation yields high quality inference approximation for general CBI problems like Max CSPs. Finally, we discuss the possibilities of integrating stochastic approaches into our semiring-based CBI framework. We also discuss contextspecific inference with backtracking as a promising inference approach for general CBI problems. In general, we are aiming at studying the most important common characteristics of various CBI problems, borrowing design ideas from other fields based on the analyses and comparison of different inference approaches, and significantly reducing the amount of implementation work targetted previously at the individual problems.