Jacek Kisynski

Peter Carbonetto, Jacek Kisynski, Nando de Freitas et al.

The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation. This paper extends BLOG by adopting generative processes over function spaces - known as nonparametrics in the Bayesian literature. We introduce syntax for reasoning about arbitrary collections of objects, and their properties, in an intuitive manner. By exploiting exchangeability, distributions over unknown objects and their attributes are cast as Dirichlet processes, which resolve difficulties in model selection and inference caused by varying numbers of objects. We demonstrate these concepts with application to citation matching.

Jacek Kisynski, David L Poole

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference from the perspective of constraint processing and, through this viewpoint, we analyze and compare existing approaches and expose their advantages and limitations. Our theoretical results show that the wrong choice of constraint processing method can lead to exponential increase in computational complexity. Our empirical tests confirm the importance of constraint processing in lifted inference. This is the first theoretical and empirical study of constraint processing in lifted inference.