Related papers: On the Optimal Reconstruction of Partially Observe…
Regressing a scalar response on a random function is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression based on a projection approach a prominent method for solving…
In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…
We develop algorithms for detecting multiple changepoints in functional data when the number of changepoints is unknown (unsupervised case), when it is specified apriori (supervised case), and when certain bounds are available…
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
We propose a novel estimator of the autocorrelation function in presence of missing observations. We establish the consistency, the asymptotic normality, and we derive deviation bounds for various classes of weakly dependent stationary time…
Deep reinforcement learning algorithms that estimate state and state-action value functions have been shown to be effective in a variety of challenging domains, including learning control strategies from raw image pixels. However,…
Existing identification and estimation methods for semiparametric sample selection models rely heavily on exclusion restrictions. However, it is difficult in practice to find a credible excluded variable that has a correlation with…
In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…
Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…
In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in the aggregate models a desired property of the ideal solution…
This paper is concerned with function reconstruction from samples. The sampling points used in several approaches are (1) structured points connected with fast algorithms or (2) unstructured points coming from, e.g., an initial random draw…
We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics…
Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Prior knowledge about the imaging physics provides a mechanistic forward operator that plays an important role in image reconstruction, although myriad sources of possible errors in the operator could negatively impact the reconstruction…
We establish minimax optimal rates of convergence for nonparametric estimation in functional ANOVA models when data from first-order partial derivatives are available. Our results reveal that partial derivatives can improve convergence…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…