Sequential Co-Sparse Factor Regression.

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• Sparse singular value decomposition (SVD) is valuable for dimensionality reduction in multivariate regression.
• Existing methods face challenges due to orthogonality constraints and co-sparsity regularization.

Purpose of the Study:

• To develop an efficient computational procedure for sparse SVD in multivariate regression.
• To address the challenges posed by orthogonality and co-sparsity.
• To improve interpretability of high-dimensional data.

Main Methods:

• Reformulated the problem as supervised co-sparse factor analysis.
• Developed sequential factor extraction via co-sparse unit-rank estimation (SeCURE).
• Bypassed orthogonality requirements, reducing each step to sparse multivariate regression with a unit-rank constraint.

Main Results:

• SeCURE ensures convergence and efficient computation, even with incomplete data.
• Latent factors are sparse linear combinations of predictors, influencing subsets of responses.
• Asymptotic oracle properties and non-asymptotic error bounds were established for estimators.

Conclusions:

• SeCURE offers an effective and efficient approach to sparse SVD in multivariate regression.
• The method enhances data interpretation by identifying sparse latent factors.
• Demonstrated efficacy through simulations and genetic data applications.