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We introduce a dynamic generative model, Bayesian allocation model (BAM),which establishes explicit connections between nonnegative tensor factorization(NTF), graphical models of discrete probability distributions and theirBayesian extensions, and the topic models such as the latent Dirichletallocation. BAM is based on a Poisson process, whose events are marked by usinga Bayesian network, where the conditional probability tables of this networkare then integrated out analytically. We show that the resulting marginalprocess turns out to be a Polya urn, an integer valued self-reinforcingprocess. This urn processes, which we name a Polya-Bayes process, obey certainconditional independence properties that provide further insight about thenature of NTF. These insights also let us develop space efficient simulationalgorithms that respect the potential sparsity of data: we propose a class ofsequential importance sampling algorithms for computing NTF and approximatingtheir marginal likelihood, which would be useful for model selection. Theresulting methods can also be viewed as a model scoring method for topic modelsand discrete Bayesian networks with hidden variables. The new algorithms havefavourable properties in the sparse data regime when contrasted withvariational algorithms that become more accurate when the total sum of theelements of the observed tensor goes to infinity. We illustrate the performanceon several examples and numerically study the behaviour of the algorithms forvarious data regimes.

Bayesian Allocation Model: Inference by Sequential Monte Carlo for Nonnegative Tensor Factorizations and Topic Models using Polya Urns