Related papers: On Iterative Hard Thresholding Methods for High-di…
We study asymptotically normal estimation and confidence regions for low-dimensional parameters in high-dimensional sparse models. Our approach is based on the $\ell_1$-penalized M-estimator which is used for construction of a bias…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
Hilbert-Schmidt Independence Criterion (HSIC) has recently been used in the field of single-index models to estimate the directions. Compared with some other well-established methods, it requires relatively weaker conditions. However, its…
Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized…
Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (2016; JMLR) based on randomized sketching matrices. However, it is computationally…
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
Hard Thresholding Pursuit (HTP) has aroused increasing attention for its robust theoretical guarantees and impressive numerical performance in non-convex optimization. In this paper, we introduce a novel tuning-free procedure, named…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Sparse representation of a single measurement vector (SMV) has been explored in a variety of compressive sensing applications. Recently, SMV models have been extended to solve multiple measurement vectors (MMV) problems, where the…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
High-dimensional linear regression with interaction effects is broadly applied in research fields such as bioinformatics and social science. In this paper, we first investigate the minimax rate of convergence for regression estimation in…
Sparse variable selection improves interpretability and generalization in high-dimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale…
The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…