Jul 12, 2020
Sparse principal component analysis (PCA) is a widely-used dimensionality reduction tool in statistics and machine learning. Most methods mentioned in literature are either heuristics for good primal feasible solutions under statistical assumptions or ADMM-type algorithms with stationary/critical points convergence property for the regularized reformulation of sparse PCA. However, none of these methods can efficiently verify the quality of the solutions via comparing current objective values with their dual bounds, especially in model-free case. We propose a new framework that finds out upper (dual) bounds for the sparse PCA within polynomial time via solving a convex integer program (IP). We show that, in the worst-case, the dual bounds provided by the convex IP is within an affine function of the global optimal value. Moreover, in contrast to the semi-definition relaxation, this framework is much easier to scale on large cases. Numerical results on both artificial and real cases are reported to demonstrate the advantages of our method.
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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