  Predicting user affinity to items is an important problem in applications
like content optimization, computational advertising, and many more. While
bilinear random effect models (matrix factorization) provide state-of-the-art
performance when minimizing RMSE through a Gaussian response model on explicit
ratings data, applying it to imbalanced binary response data presents
additional challenges that we carefully study in this paper. Data in many
applications usually consist of users' implicit response that are often binary
-- clicking an item or not; the goal is to predict click rates, which is often
combined with other measures to calculate utilities to rank items at runtime of
the recommender systems. Because of the implicit nature, such data are usually
much larger than explicit rating data and often have an imbalanced distribution
with a small fraction of click events, making accurate click rate prediction
difficult. In this paper, we address two problems. First, we show previous
techniques to estimate bilinear random effect models with binary data are less
accurate compared to our new approach based on adaptive rejection sampling,
especially for imbalanced response. Second, we develop a parallel bilinear
random effect model fitting framework using Map-Reduce paradigm that scales to
massive datasets. Our parallel algorithm is based on a "divide and conquer"
strategy coupled with an ensemble approach. Through experiments on the
benchmark MovieLens data, a small Yahoo! Front Page data set, and a large
Yahoo! Front Page data set that contains 8M users and 1B binary observations,
we show that careful handling of binary response as well as identifiability
issues are needed to achieve good performance for click rate prediction, and
that the proposed adaptive rejection sampler and the partitioning as well as
ensemble techniques significantly improve model performance.
