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From an optimizer's perspective, achieving the global optimum for a general nonconvex problem is often provably NP-hard using the classical worst-case analysis. In the case of Cox's proportional hazards model, by taking its statistical…

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96…

Induction benefits from useful priors. Penalized regression approaches, like ridge regression, shrink weights toward zero but zero association is usually not a sensible prior. Inspired by simple and robust decision heuristics humans use, we…

It becomes an interesting problem to identify subgroup structures in data analysis as populations are probably heterogeneous in practice. In this paper, we consider M-estimators together with both concave and pairwise fusion penalties,…

In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…

We study the problem of estimating the mean of a distribution in high dimensions when either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent developments in robust statistics have established efficient…

Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily…

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…

In this paper we consider high dimension models based on dependent observations defined through autoregressive processes. For such models we develop an adaptive efficient estimation method via the robust sequential model selection…

We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…

Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…

This paper considers the problem of estimation in the generalized semiparametric model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is…

We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex…

We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is…

In high dimensional regression, where the number of covariates is of the order of the number of observations, ridge penalization is often used as a remedy against overfitting. Unfortunately, for correlated covariates such regularisation…

Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…

High-dimensional regression and regression with a left-censored response are each well-studied topics. In spite of this, few methods have been proposed which deal with both of these complications simultaneously. The Tobit model -- long the…

In many high-dimensional prediction or classification tasks, complementary data on the features are available, e.g. prior biological knowledge on (epi)genetic markers. Here we consider tasks with numerical prior information that provide an…

We introduce an original method of multidimensional ridge penalization in functional local linear regressions. The nonparametric regression of functional data is extended from its multivariate counterpart, and is known to be sensitive to…