Related papers: An RKHS approach for pivotal inference in function…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of $L_p$-type functionals of kernel estimators $(1 \leq p < \infty)$. Drawing on the approach of…
Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…
In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under high-dimensional multivariate functional data setting.…
Data loss is a critical problem in structural health monitoring (SHM). Probability distributions play a highly important role in many applications. Improving the quality of distribution estimations made using incomplete samples is highly…
In this paper, we study an online learning algorithm with a robust loss function $\mathcal{L}_{\sigma}$ for regression over a reproducing kernel Hilbert space (RKHS). The loss function $\mathcal{L}_{\sigma}$ involving a scaling parameter…
A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test the nullity or linearity of the effect of the…
We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W, i.e., an exogenous random function, a scalar response Y is modeled in dependence of an…
We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a…
No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient,…
We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed.…
The slope coefficient in a rank-rank regression is a popular measure of intergenerational mobility. In this article, we first show that commonly used inference methods for this slope parameter are invalid. Second, when the underlying…
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed…
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…