Personalized Prediction and Sparsity Pursuit in Latent Factor Models

Abstract

Personalized information filtering extracts the information specifically relevant to a user, predicting his/her preference over a large number of items, based on the opinions of users who think alike or its content. This problem is cast into the framework of regression and classification, where we integrate additional user-specific and content-specific predictors in partial latent models, for higher predictive accuracy. In particular, we factorize a user-over-item preference matrix into a product of two matrices, each representing a user’s preference and an item preference by users. Then we propose a likelihood method to seek a sparsest latent factorization, from a class of overcomplete factorizations, possibly with a high percentage of missing values. This promotes additional sparsity beyond rank reduction. Computationally, we design methods based on a “decomposition and combination” strategy, to break large-scale optimization into many small subproblems to solve in a recursive and parallel manner. On this basis, we implement the proposed methods through multi-platform shared-memory parallel programming, and through Mahout, a library for scalable machine learning and data mining, for mapReduce computation. For example, our methods are scalable to a dataset consisting of three billions of observations on a single machine with sufficient memory, having good timings. Both theoretical and numerical investigations show that the proposed methods exhibit a significant improvement in accuracy over state-of-the-art scalable methods. Supplementary materials for this article are available online.

• Alternating directions
• Collaborative filtering
• Content-based filtering
• Partial latent models
• Recommender
• Sparse factorization.