CHR(PRISM)-based Probabilistic Logic Learning

PRISM is an extension of Prolog with probabilistic predicates and built-in support for expectation-maximization learning. Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules. In this paper, we introduce a new probabilistic logic formalism, called CHRiSM, based on a combination of CHR and PRISM. It can be used for high-level rapid prototyping of complex statistical models by means of "chance rules". The underlying PRISM system can then be used for several probabilistic inference tasks, including probability computation and parameter learning. We define the CHRiSM language in terms of syntax and operational semantics, and illustrate it with examples. We define the notion of ambiguous programs and define a distribution semantics for unambiguous programs. Next, we describe an implementation of CHRiSM, based on CHR(PRISM). We discuss the relation between CHRiSM and other probabilistic logic programming languages, in particular PCHR. Finally we identify potential application domains

Comparing models of symbolic music using probabilistic grammars and probabilistic programming

We conduct a systematic comparison of several probabilistic models of symbolic music, including zeroth and first order Markov models over pitches and intervals, a hidden Markov model over pitches, and a probabilistic context free grammar with two parameterisations, all implemented uniformly using a probabilistic programming language (PRISM). This allows us to take advantage of variational Bayesian methods for learning parameters and assessing the goodness of fit of the models in a principled way. When applied to a corpus of Bach chorales and the Essen folk song collection, we show that, depending on various parameters, the probabilistic grammars sometimes but not always out-perform the simple Markov models. On looking for evidence of over- fitting of complex models to small datasets, we find that even the smallest dataset is sufficient to support the richest parameterisation of the probabilistic grammars. However, examining how the models perform on smaller subsets of pieces, we find that the simpler Markov models do indeed out-perform the best grammar-based model at the small end of the scale

Probabilistic-logical modeling of music

PRISM is a probabilistic-logical programming language based on Prolog. We present a PRISM-implementation of a general model for polyphonic music, based on Hidden Markov Models. Its probability parameters are automatically learned by running the built-in EM-algorithm of PRISM on training examples. We show how the model can be used as a classifier for music that guesses the composer of unknown fragments of music. Then we use it to automatically compose new music.status: publishe