Related papers: Computing Functions of Random Variables via Reprod…
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 provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable…
We use a classical characterisation to prove that functions which are bounded away from zero cannot be elements of reproducing kernel Hilbert spaces whose reproducing kernels decays to zero in a suitable way. The result is used to study…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…
This paper explores methods for estimating or approximating the total variation distance and the chi-squared divergence of probability measures within topological sample spaces, using independent and identically distributed samples. Our…
We consider the theory of bond discounts, defined as the difference between the terminal payoff of the contract and its current price. Working in the setting of finite-dimensional realizations in the HJM framework, under suitable notions of…
Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models…
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…
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,…
We show how the Riemann-Hilbert problem can be used to compute correlation kernels for determinantal point processes arising in different models of asymptotic combinatorics and representation theory. The Whittaker kernel and the discrete…
In this work, we develop and study an empirical projection operator scheme for solving nonparametric regression problems. This scheme is based on an approximate projection of the regression function over a suitable reproducing kernel…
We propose a novel procedure for estimating and conducting inference on average marginal effects in partially linear instrumental regressions using Reproducing Kernel Hilbert Space methods. Our procedure relies on a single regularization…