Approximation Bounds for Sparse Principal Component Analysis
Alexandre d'Aspremont, Francis Bach, Laurent El Ghaoui
TL;DR
This paper establishes approximation bounds for a semidefinite programming approach to sparse principal component analysis, aiding in hypothesis testing for Gaussian models with sparse signals.
Contribution
It provides the first theoretical approximation bounds for SDP relaxations in sparse PCA, improving understanding of their effectiveness.
Findings
Bounds on approximation ratios for SDP relaxations
Enhanced hypothesis testing methods for Gaussian models
Theoretical guarantees for sparse PCA algorithms
Abstract
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are sampled from Gaussian models with a single sparse leading component.
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Taxonomy
TopicsGaussian Processes and Bayesian Inference · Stochastic Gradient Optimization Techniques · Statistical Methods and Inference