Parameter Learning in PRISM Programs with Continuous Random Variables
  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.
