Related papers: Ultrahigh-dimensional Robust and Efficient Sparse …
By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…
The mainstream theory of hypothesis testing in high-dimensional regression typically assumes the underlying true model is a low-dimensional linear regression model, yet the Box-Cox transformation is a regression technique commonly used to…
We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…
High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of the rank loss brings great challenges to the computation. To…
We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…
Penalized regression estimators are a popular tool for the analysis of sparse and high-dimensional data sets. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection,…
We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback penalty is a weakly convex function. It bears various…
This paper investigates quantile regression in the presence of non-convex and non-smooth sparse penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). The non-smooth and non-convex nature of…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated…
$\ell_1$ penalized quantile regression is used in many fields as an alternative to penalized least squares regressions for high-dimensional data analysis. Existing algorithms for penalized quantile regression either use linear programming,…
Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low-rank matrix completion. Also in unsupervised learning one often relies on imputation methods. As a matter of fact,…