Related papers: Functional Partial Least-Squares: Adaptive Estimat…
We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…
We revisit the problem of fair representation learning by proposing Fair Partial Least Squares (PLS) components. PLS is widely used in statistics to efficiently reduce the dimension of the data by providing representation tailored for the…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
This paper considers adaptive, minimax estimation of a quadratic functional in a nonparametric instrumental variables (NPIV) model, which is an important problem in optimal estimation of a nonlinear functional of an ill-posed inverse…
Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…
Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which…
We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
We study a minimax risk of estimating inverse functions on a plane, while keeping an estimator is also invertible. Learning invertibility from data and exploiting an invertible estimator are used in many domains, such as statistics,…
Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…
We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and…
We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
In the heteroscedastic linear model, the weighted least squares (WLS) estimate of the model coefficients is more efficient than the ordinary least squares (OLS) esti- mate. However, the practical application of WLS is challenging because it…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…