The paper presents a method for uncertainty propagation in Bayesian networks in symbolic, as opposed to numeric, form. The algebraic structure of probabilities is characterized. The prior probabilities of instantiations and the marginal probabilities are shown to be rational functions of the parameters, where the polynomials appearing in the numerator and the denominator are at the most first d...

We define two non-parametric models for Sum-Product Networks (SPNs) (Poon & Domingos, 2011). The first is a tree structure of Dirichlet Processes; the second is a dag of hierarchical Dirichlet Processes. These generative models for data implicitly define a prior distribution on SPN of tree and of dag structure. They allow MCMC fitting of data to SPN models, and the learning of SPN structure fro...

Shannon’s entropy is a basic quantity in information theory, and a fundamental building block for the analysis of neural codes. Estimating the entropy of a discrete distribution from samples is an important and difficult problem that has received considerable attention in statistics and theoretical neuroscience. However, neural responses have characteristic statistical structure that generic en...

We consider the inference problem of estimating covariate and genetic effects in a family-based case-control study where families are ascertained on the basis of the number of cases within the family. However, our interest lies not only in estimating the fixed covariate effects but also in estimating the random effects parameters that account for varying correlations among family members. These...