Related papers: Nonparametric Regression with Adaptive Truncation …

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…

We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…

Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…

Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…

Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

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…

It is often of interest to estimate regression functions non-parametrically. Penalized regression (PR) is one statistically-effective, well-studied solution to this problem. Unfortunately, in many cases, finding exact solutions to PR…

In this paper we study nonconvex penalization using Bernstein functions. Since the Bernstein function is concave and nonsmooth at the origin, it can induce a class of nonconvex functions for high-dimensional sparse estimation problems. We…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…

For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…

Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to…