Related papers: Nearly optimal minimax estimator for high-dimensio…

We consider a convex constrained Gaussian sequence model and characterize necessary and sufficient conditions for the least squares estimator (LSE) to be minimax optimal. For a closed convex set $K\subset \mathbb{R}^n$ we observe…

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…

We consider solving the $\ell_1$-regularized least-squares ($\ell_1$-LS) problem in the context of sparse recovery, for applications such as compressed sensing. The standard proximal gradient method, also known as iterative…

Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…

The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…

For the Gaussian sequence model, we obtain non-asymptotic minimax rates of estimation of the linear, quadratic and the L2-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main…

In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…

The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…

In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…

In this paper, we study the minimax rates and provide an implementable convex algorithm for Poisson inverse problems under weak sparsity and physical constraints. In particular we assume the model $y_i \sim \mbox{Poisson}(Ta_i^{\top}f^*)$…

In this paper we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^d$ with $d\ge 2$ and $N(0,1)$ noise, the minimax rate for the $\ell_2$ risk is known to be bounded…

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…

We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…

We propose a new sparse estimation method, termed MIC (Minimum approximated Information Criterion), for generalized linear models (GLM) in fixed dimensions. What is essentially involved in MIC is the approximation of the $\ell_0$-norm with…

We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…

We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the exact minimax prediction and $\ell_2$ estimation rate $(s/n)\log (p/s)$ in high-dimensional…

We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…