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Personalized Prediction and Sparsity Pursuit in Latent Factor Models

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  • Yunzhang Zhu
  • Xiaotong Shen
  • Changqing Ye

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.

Suggested Citation

  • Yunzhang Zhu & Xiaotong Shen & Changqing Ye, 2016. "Personalized Prediction and Sparsity Pursuit in Latent Factor Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 241-252, March.
  • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:241-252
    DOI: 10.1080/01621459.2014.999158
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    Cited by:

    1. Chen, Yunxiao & Li, Xiaoou, 2022. "Determining the number of factors in high-dimensional generalized latent factor models," LSE Research Online Documents on Economics 111574, London School of Economics and Political Science, LSE Library.
    2. Dong, Ruipeng & Li, Daoji & Zheng, Zemin, 2021. "Parallel integrative learning for large-scale multi-response regression with incomplete outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    3. Yoav Bergner & Peter Halpin & Jill-Jênn Vie, 2022. "Multidimensional Item Response Theory in the Style of Collaborative Filtering," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 266-288, March.
    4. Chen, Yunxiao & Li, Xiaoou & Zhang, Siliang, 2019. "Structured latent factor analysis for large-scale data: identifiability, estimability, and their implications," LSE Research Online Documents on Economics 101122, London School of Economics and Political Science, LSE Library.

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