2018/09/17 by Kean Ming Tan, Zhaoran Wang, Tan, Kean Ming +7
Engineering · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1809.06024
openalex publication_date 2018/09/17 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
Sliced inverse regression is a popular tool for sufficient dimension\nreduction, which replaces covariates with a minimal set of their linear\ncombinations without loss of information on the conditional distribution of the\nresponse given the covariates. The estimated linear combinations include all\ncovariates, making results difficult to interpret and perhaps unnecessarily\nvariable, particularly when the number of covariates is large. In this paper,\nwe propose a convex formulation for fitting sparse sliced inverse regression in\nhigh dimensions. Our proposal estimates the subspace of the linear combinations\nof the covariates directly and performs variable selection simultaneously. We\nsolve the resulting convex optimization problem via the linearized alternating\ndirection methods of multiplier algorithm, and establish an upper bound on the\nsubspace distance between the estimated and the true subspaces. Through\nnumerical studies, we show that our proposal is able to identify the correct\ncovariates in the high-dimensional setting.\n