Related papers: Functional Inverse Regression in an Enlarged Dimen…
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares…
Advancements in modern science have led to an increased prevalence of functional data, which are usually viewed as elements of the space of square-integrable functions $L^2$. Core methods in functional data analysis, such as functional…
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 + {\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…
The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator…
We discuss new proofs, and new forms, of a reverse logarithmic Sobolev inequality, with respect to the standard Gaussian measure, for low complexity functions, measured in terms of Gaussian-width. In particular, we provide a dimension-free…
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…
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…
We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…
In this paper, we prove that functional sliced inverse regression (FSIR) achieves the optimal (minimax) rate for estimating the central space in functional sufficient dimension reduction problems. First, we provide a concentration…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…