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This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…
This paper studies statistical aggregation procedures in the regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types…
In this paper, we present a study of a kernel-based consensual aggregation on randomly projected high-dimensional features of predictions for regression. The aggregation scheme is composed of two steps: the high-dimensional features of…
We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients…
We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and…
Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed…
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…
For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…
This article considers a linear model in a high dimensional data scenario. We propose a process which uses multiple loss functions both to select relevant predictors and to estimate parameters, and study its asymptotic properties. Variable…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, non-linearities…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…
Given noisy data, function estimation is considered when the unknown function is known apriori to consist of a small number of regions where the function is either convex or concave. When the regions are known apriori, the estimate is…