6,105 research outputs found
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
Bayesian semi non-negative matrix factorisation
Non-negative Matrix Factorisation (NMF) has become a standard method for source identification when data, sources and mixing coefficients are constrained to be positive-valued. The method has recently been extended to allow for negative-valued data and sources in the form of Semi-and Convex-NMF. In this paper, we re-elaborate Semi-NMF within a full Bayesian framework. This provides solid foundations for parameter estimation and, importantly, a principled method to address the problem of choosing the most adequate number of sources to describe the observed data. The proposed Bayesian Semi-NMF is preliminarily evaluated here in a real neuro-oncology problem.Peer ReviewedPostprint (published version
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