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Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…

The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse…

This paper considers inference in a linear regression model with random right censoring and outliers. The number of outliers can grow with the sample size while their proportion goes to zero. The model is semiparametric and we make only…

In the context of undirected Gaussian graphical models, we introduce three estimators based on elastic net penalty for the underlying dependence graph. Our goal is to estimate the sparse precision matrix, from which to retrieve both the…

In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…

Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which…

Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…

Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate…

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive…

Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…

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…

The multi-label classification framework, where each observation can be associated with a set of labels, has generated a tremendous amount of attention over recent years. The modern multi-label problems are typically large-scale in terms of…

We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading…

Sparse logistic regression, as an effective tool of classification, has been developed tremendously in recent two decades, from its origination the $\ell_1$-regularized version to the sparsity constrained models. This paper is carried out…

The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…