Computationally Efficient Robust Estimation of Sparse Functionals
It addresses the sensitivity of statistical procedures to modeling deviations in high-dimensional data, offering a robust solution for sparse functional estimation.
The paper tackles the problem of robust estimation of sparse functionals in high-dimensional settings where dimensions can exceed sample size, providing a computationally and statistically efficient algorithm that guarantees accurate recovery under unified deterministic conditions, applicable to models like sparse mean and covariance estimation, linear regression, and generalized linear models.
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse functionals, and provide a computationally and statistically efficient algorithm in the high-dimensional setting. Our theory identifies a unified set of deterministic conditions under which our algorithm guarantees accurate recovery. By further establishing that these deterministic conditions hold with high-probability for a wide range of statistical models, our theory applies to many problems of considerable interest including sparse mean and covariance estimation; sparse linear regression; and sparse generalized linear models.