Exploiting Causal Independence in Bayesian Network Inference

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as ``or'', ``sum'' or ``max'', on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.Comment: See http://www.jair.org/ for any accompanying file

Mining data quality rules based on T-dependence

Since their introduction in 1976, edit rules have been a standard tool in statistical analysis. Basically, edit rules are a compact representation of non-permitted combinations of values in a dataset. In this paper, we propose a technique to automatically find edit rules by use of the concept of T-dependence. We first generalize the traditional notion of lift, to that of T-lift, where stochastic independence is generalized to T-dependence. A combination of values is declared as an edit rule under a t-norm T if there is a strong negative correlation under T-dependence. We show several interesting properties of this approach. In particular, we show that under the minimum t-norm, edit rules can be computed efficiently by use of frequent pattern trees. Experimental results show that there is a weak to medium correlation in the rank order of edit rules obtained under T_M and T_P, indicating that the semantics of these kinds of dependencies are different