Generalized linear model (GLM) is a widely used class of models for statistical inference and response prediction problems. For instance, in order to recommend relevant content to a user or optimize for revenue, many web companies use logistic regression models to predict the probability of the user's clicking on an item (e.g., ad, news article, job). In scenarios where the data is abundant, having a more fine-grained model at the user or item level would potentially lead to more accurate prediction, as the user's personal preferences on items and the item's specific attraction for users can be better captured. One common approach is to introduce ID-level regression coefficients in addition to the global regression coefficients in a GLM setting, and such models are called generalized linear mixed models (GLMix) in the statistical literature. However, for big data sets with a large number of ID-level coefficients, fitting a GLMix model can be computationally challenging. In this paper, we report how we successfully overcame the scalability bottleneck by applying parallelized block coordinate descent under the Bulk Synchronous Parallel (BSP) paradigm. We deployed the model in the LinkedIn job recommender system, and generated 20% to 40% more job applications for job seekers on LinkedIn.

A new methodology is developed for joint analysis of a matrix and accompanying documents, with the documents associated with the matrix rows/columns. The documents are modeled with a focused topic model, inferring latent binary features (topics) for each document. A new matrix decomposition is developed, with latent binary features associated with the rows/columns, and with imposition of a low-rank constraint. The matrix decomposition and topic model are coupled by sharing the latent binary feature vectors associated with each. The model is applied to roll-call data, with the associated documents defined by the legislation. State-of-the-art results are manifested for prediction of votes on a new piece of legislation, based only on the observed text legislation. The coupling of the text and legislation is also demonstrated to yield insight into the properties of the matrix decomposition for roll-call data.

The nested Chinese restaurant process is extended to design a nonparametric topic-model tree for representation of human choices. Each tree branch corresponds to a type of person, and each node (topic) has a corresponding probability vector over items that may be selected. The observed data are assumed to have associated temporal covariates (corresponding to the time at which choices are made), and we wish to impose that with increasing time it is more probable that topics deeper in the tree are utilized. This structure is imposed by developing a new “change point" stick-breaking model that is coupled with a Poisson and product-of-gammas construction. To share topics across the tree nodes, topic distributions are drawn from a Dirichlet process. As a demonstration of this concept, we analyze real data on course selections of undergraduate students at Duke University, with the goal of uncovering and concisely representing structure in the curriculum and in the characteristics of the student body.