Gopalan, Prem K (Princeton University) “Scalable inference of discrete data: User behavior, networks and genetic variation” (2015)

Gopalan, Prem K (Princeton University) “Scalable inference of discrete data: User behavior, networks and genetic variation” (2015) Advisor: Blei, David M.

Recent years have seen explosive growth in data, models and computation. Massive data sets and sophisticated probabilistic models are increasingly used in the fields of high-energy physics, biology, genetics and in personalization applications; however, many statistical algorithms remain inefficient, impeding scientific progress.

In this thesis, we present several efficient statistical algorithms for learning from massive discrete data sets. We focus on discrete data because complex and structured activity such as chromosome folding in three dimensions, human genetic variation, social network interactions and product ratings are often encoded as simple matrices of discrete numerical observations. Our algorithms derive from a Bayesian perspective and lie in the framework of directed graphical models and mean-field variational inference. Situated in this framework, we gain computational and statistical efficiency through modeling insights and through subsampling informative data during inference.

We begin with additive Poisson factorization models for recommending items to users based on user consumption or ratings. These models provide sparse latent representations of users and items, and capture the long-tailed distributions of user consumption. We use them as building blocks for article recommendation models by sharing latent spaces across readership and article text. We demonstrate that our algorithms scale to massive data sets, are easy to implement and provide competitive user recommendations. Then, we develop a Bayesian nonparametric model in which the latent representations of users and items grow to accommodate new data.

In the second part of the thesis, we develop novel algorithms for discovering overlapping communities in large networks. These algorithms interleave non-uniform subsampling of the network with model estimation. Our network models capture the basic ways in which nodes connect to each other, through similarity and popularity, using mixed-memberships representations and generalized linear model formulation.

Finally, we present the TeraStructure algorithm to fit Bayesian models of genetic variation in human populations on tera-sample-sized data sets (1012 observed genotypes, e.g, 1M individuals at 1M SNPs). On real genomic data collected from thousands of individuals, TeraStructure is faster than existing methods and recovers the latent population structure with equal accuracy. On genomic data simulated at the tera-sample-size scales, TeraStructure is highly accurate and is the only method that can complete its analysis.

For details, please visit the thesis page.