Hybrid Probabilistic Inference with Logical Constraints: Tractability and Message Passing
Research Scholar, StarAI Lab, UCLA, 2019
- Advisor: Prof. Guy Van den Broeck
- Date: Jul 2019 - Sep 2019
- Studied the basic theories and algorithms of Modeling and Reasoning with Bayesian Networks
- Proposed the moment calculation algorithm of the SMT($\mathcal{LRA}$) random variables for Weighted Model Integration (WMI), Derived the marginal probability density function for WMI
- Improved the numerical integration step for the algorithm of efficient search-based WMI using Gaussian quadrature rules
- Devised a novel formulation of MI via an exact message passing scheme on the tractable MI problems adopting symbolic integration, which is able to exactly compute all the variable marginal densities – as well as statistical moments – at once
- Proved the correctness and the amortization of message passing MI algorithm
- Analyzed the treewidth and diameter of the primal graph when the reduction from tree-shaped WMI with bivariate queries to MI played
- Constructed a representative example and Elaborated the procedure of the reduction from WMI to MI, passing by WMI$_{\mathbb{R}}$, including both boolean and continuous variables, both disjunction and conjunction
- Finished the paper-writing on this work and posted the paper to arXiv as joint first author