Related papers: Variable Selection and Minimax Prediction in High-…

Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional $\mathbf{\mu}^T \mathbf{\Sigma}^{-1} \mathbf{\mu}$ involving both the mean vector $\mathbf{\mu}$ and covariance matrix…

This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…

This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null…

This paper develops a novel spatial quantile function-on-scalar regression model, which studies the conditional spatial distribution of a high-dimensional functional response given scalar predictors. With the strength of both quantile…

This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…

Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the…

We consider the high-dimensional heteroscedastic regression model, where the mean and the log variance are modeled as a linear combination of input variables. Existing literature on high-dimensional linear regres- sion models has largely…

In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…

In this paper we consider the linear regression model $Y =S X+\varepsilon $ with functional regressors and responses. We develop new inference tools to quantify deviations of the true slope $S$ from a hypothesized operator $S_0$ with…

Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional…

We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…

We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…

We study two classes of extension problems, and their interconnections: (i) Extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; (ii) In case of Lie groups, representations of the…

Estimation of linear functionals from observed data is an important task in many subjects. Juditsky & Nemirovski [The Annals of Statistics 37.5A (2009): 2278-2300] propose a framework for non-parametric estimation of linear functionals in a…

We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ type arise naturally as solutions of regularized neural network learning problems and…

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…

This work focuses on the issue of variable selection in functional regression. Unlike most work in this framework, our approach does not select isolated points in the definition domain of the predictors, nor does it rely on the expansion of…

Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…

We delve into the estimation of the functional coefficients and inference for varying coefficient model. Applying Laguerre series, we develop an estimator for the vector of functional coefficients that attains asymptotically optimal…