Related papers: Inference for Additive Models in the Presence of P…
We propose a new, nonparametric approach to estimating the value function in reinforcement learning. This approach makes use of a recently developed representation of conditional distributions as functions in a reproducing kernel Hilbert…
High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each…
It is well known that nonparametric regression estimation and inference procedures are subject to the curse of dimensionality. Moreover, model interpretability usually decreases with the data dimension. Therefore, model-free variable…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…
This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…
Deviations from the center within a robust neighborhood of a parametric model distribution may naturally be considered an infinite dimensional nuisance parameter. Thus, the semiparametric method may be tried, which is to compute the scores…
This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…
We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…
A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…
This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment…
This paper proposes a new class of nonparametric tests for the correct specification of models based on conditional moment restrictions, paying particular attention to generalized propensity score models. The test procedure is based on two…
We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…
In this paper, we discuss the problem of system identification when frequency domain side information is available on the system. Initially, we consider the case where the prior knowledge is provided as being the $\Hcal_{\infty}$-norm of…
We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function…
Reproducing kernel Hilbert spaces (RKHSs) are key spaces for machine learning that are becoming popular also for linear system identification. In particular, the so-called stable RKHSs can be used to model absolutely summable impulse…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
In applied settings, tests of hypothesis where a nuisance parameter is only identifiable under the alternative often reduces into one of Testing One Hypothesis Multiple times (TOHM). Specifically, a fine discretization of the space of the…