Parameter Learning in PRISM Programs with Continuous Random Variables
This work addresses a limitation in probabilistic logic programming for researchers and practitioners by allowing continuous variables, though it is incremental as it builds on existing PRISM frameworks.
The paper tackles the problem of parameter learning in probabilistic logic programming (PRISM) by extending it to support Gaussian random variables and linear equality constraints, enabling the encoding of models like finite mixtures and Kalman filters, and develops an EM-based algorithm that learns distribution parameters without enumeration, generalizing methods from PRISM and Hybrid Bayesian Networks.
Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, De Raedt et al's ProbLog and Vennekens et al's LPAD, combines statistical and logical knowledge representation and inference. Inference in these languages is based on enumerative construction of proofs over logic programs. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we extend PRISM with Gaussian random variables and linear equality constraints, and consider the problem of parameter learning in the extended language. Many statistical models such as finite mixture models and Kalman filter can be encoded in extended PRISM. Our EM-based learning algorithm uses a symbolic inference procedure that represents sets of derivations without enumeration. This permits us to learn the distribution parameters of extended PRISM programs with discrete as well as Gaussian variables. The learning algorithm naturally generalizes the ones used for PRISM and Hybrid Bayesian Networks.