Related papers: Data-driven calibration of penalties for least-squ…

In the context of high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where the penalty…

Many popular piecewise regression models rely on minimizing a cost function on the model fit with a linear penalty on the number of segments. However, this penalty does not take into account varying complexities of the model functions on…

The IBOSS approach proposed by Wang et al. (2019) selects the most informative subset of n points. It assumes that the ordinary least squares method is used and requires that the number of variables, p, is not large. However, in many…

Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…

Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…

Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these…

We present a linear regression method for predictions on a small data set making use of a second possibly biased data set that may be much larger. Our method fits linear regressions to the two data sets while penalizing the difference…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

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…

The `Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a…

Overlapping asymmetric datasets are common in data science and pose questions of how they can be incorporated together into a predictive analysis. In healthcare datasets there is often a small amount of information that is available for a…

The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection…

The Huber's criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. In the case of small sample size…

Penalized smoothing is a standard tool in regression analysis. Classical approaches often rely on basis or kernel expansions, which constrain the estimator to a fixed span and impose smoothness assumptions that may be restrictive for…

Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight…

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…

High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…