相关论文: A Smooth and Locally Sparse Estimator for Function…

Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely…

We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…

We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…

We consider the problem of minimizing the sum of three convex functions: i) a smooth function $f$ in the form of an expectation or a finite average, ii) a non-smooth function $g$ in the form of a finite average of proximable functions…

In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing…

It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…

In this paper we provide a priori error estimates in standard Sobolev (semi-)norms for approximation in spline spaces of maximal smoothness on arbitrary grids. The error estimates are expressed in terms of a power of the maximal grid…

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…

We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm…

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…

With modern technology development, functional data are being observed frequently in many scientific fields. A popular method for analyzing such functional data is ``smoothing first, then estimation.'' That is, statistical inference such as…

We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…

Recently, sharpness-aware minimization (SAM) has attracted much attention because of its surprising effectiveness in improving generalization performance. However, compared to stochastic gradient descent (SGD), it is more prone to getting…

Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in…

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…

In this article we present a new perspective on the smooth exact penalty function proposed by Huyer and Neumaier that is becoming more and more popular tool for solving constrained optimization problems. Our approach to Huyer and Neumaier's…

This paper proposes a novel graph-based regularized regression estimator - the hierarchical feature regression (HFR) -, which mobilizes insights from the domains of machine learning and graph theory to estimate robust parameters for a…