Expectile Matrix Factorization for Skewed Data Analysis
This work addresses skewed data analysis in matrix estimation, which is incremental as it adapts an existing regression concept to a matrix factorization framework.
The paper tackles the problem of matrix factorization for skewed and extreme data, where traditional least squares methods fail to capture central tendency or tail distributions, by proposing expectile matrix factorization using asymmetric least squares. It achieves lower recovery errors than existing methods on synthetic data with skewed noise and a real-world web service response time dataset.
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and extreme data, least squares cannot explain their central tendency or tail distributions, yielding undesired estimates. In this paper, we propose \emph{expectile matrix factorization} by introducing asymmetric least squares, a key concept in expectile regression analysis, into the matrix factorization framework. We propose an efficient algorithm to solve the new problem based on alternating minimization and quadratic programming. We prove that our algorithm converges to a global optimum and exactly recovers the true underlying low-rank matrices when noise is zero. For synthetic data with skewed noise and a real-world dataset containing web service response times, the proposed scheme achieves lower recovery errors than the existing matrix factorization method based on least squares in a wide range of settings.