UCLA

On one side, symbolic methods represent our knowledge of the world, and when coupled with probabilistic reasoning, one can infer the uncertainty of unknown facts conditioned on the knowledge of known evidence. On the other side, statistical machine learning finds and infers a predictive function from vast amounts of data. To automate complex decision making, both are crucially needed. While their unification has been long pursued, the two up to now still largely remain disparate from one another. This dissertation demonstrates circuit representations are a promising symbolic-statistical synthesis. In particular, we study circuit representations across the dimensions of tractable probabilistic reasoning with and without logical constraints, structure learning from data, and classifying on image domains, namely, the main tasks across symbolic and statistical methods. And more importantly, we show those dimensions are unified for circuit representations by leveraging the same syntactic properties.