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The paper contains several theoretical results related to the weighted nonlinear least-squares problem for low-rank signal estimation, which can be considered as a Hankel structured low-rank approximation problem. A parameterization of the…

A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…

We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid…

Statistical inferences for quadratic functionals of linear regression parameter have found wide applications including signal detection, global testing, inferences of error variance and fraction of variance explained. Classical theory based…

Functional data such as curves and surfaces have become more and more common with modern technological advancements. The use of functional predictors remains challenging due to its inherent infinite-dimensionality. The common practice is to…

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…

In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing…

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…

We propose an adaptive randomized truncation estimator for Krylov subspace methods that optimizes the trade-off between the solution variance and the computational cost, while remaining unbiased. The estimator solves a constrained…

It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…

Radial Basis Function Networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs.…

Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…

We develop a Fisher-consistent redescending robust estimator for the spatial scalar-on-function regression model, where a scalar response depends on both a functional predictor and a spatial autoregressive lag. Existing estimation…

We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…

Functional variables are often used as predictors in regression problems. A commonly-used parametric approach, called {\it scalar-on-function regression}, uses the $\ltwo$ inner product to map functional predictors into scalar responses.…

This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…

The aim of this paper is to extend worst risk minimization, also called worst average loss minimization, to the functional realm. This means finding a functional regression representation that will be robust to future distribution shifts on…