Peter Carbonetto

Eric Weine, Peter Carbonetto, Rafael A. Irizarry et al.

Poisson non-negative matrix factorization (NMF) is a widely used method to find interpretable "parts-based" decompositions of count data. While many variants of Poisson NMF exist, existing methods assume that the "parts" in the decomposition combine additively. This assumption may be natural in some settings, but not in others. Here we introduce Poisson NMF with the shifted-log link function to relax this assumption. The shifted-log link function has a single tuning parameter, and as this parameter varies the model changes from assuming that parts combine additively (i.e., standard Poisson NMF) to assuming that parts combine more multiplicatively. We provide an algorithm to fit this model by maximum likelihood, and also an approximation that substantially reduces computation time for large, sparse datasets (computations scale with the number of non-zero entries in the data matrix). We illustrate these new methods on a variety of real datasets. Our examples show how the choice of link function in Poisson NMF can substantively impact the results, and how in some settings the use of a shifted-log link function may improve interpretability compared with the standard, additive link.

Peter Carbonetto, Abhishek Sarkar, Zihao Wang et al.

In an effort to develop topic modeling methods that can be quickly applied to large data sets, we revisit the problem of maximum-likelihood estimation in topic models. It is known, at least informally, that maximum-likelihood estimation in topic models is closely related to non-negative matrix factorization (NMF). Yet, to our knowledge, this relationship has not been exploited previously to fit topic models. We show that recent advances in NMF optimization methods can be leveraged to fit topic models very efficiently, often resulting in much better fits and in less time than existing algorithms for topic models. We also formally make the connection between the NMF optimization problem and maximum-likelihood estimation for the topic model, and using this result we show that the expectation maximization (EM) algorithm for the topic model is essentially the same as the classic multiplicative updates for NMF (the only difference being that the operations are performed in a different order). Our methods are implemented in the R package fastTopics.

Peter Carbonetto, Jacek Kisynski, Nando de Freitas et al.

The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation. This paper extends BLOG by adopting generative processes over function spaces - known as nonparametrics in the Bayesian literature. We introduce syntax for reasoning about arbitrary collections of objects, and their properties, in an intuitive manner. By exploiting exchangeability, distributions over unknown objects and their attributes are cast as Dirichlet processes, which resolve difficulties in model selection and inference caused by varying numbers of objects. We demonstrate these concepts with application to citation matching.