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Functional linear and single-index models are core regression methods in functional data analysis and are widely used for performing regression in a wide range of applications when the covariates are random functions coupled with scalar…

Operator-Valued Kernels (OVKs) and associated vector-valued Reproducing Kernel Hilbert Spaces provide an elegant way to extend scalar kernel methods when the output space is a Hilbert space. Although primarily used in finite dimension for…

Learning the governing equations from time-series data has gained increasing attention due to its potential to extract useful dynamics from real-world data. Despite significant progress, it becomes challenging in the presence of noise,…

Many machine learning approaches for decision making, such as reinforcement learning, rely on simulators or predictive models to forecast the time-evolution of quantities of interest, e.g., the state of an agent or the reward of a policy.…

This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…

Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…

Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling,…

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed and discussed. An…

We propose a new, nonparametric approach to learning and representing transition dynamics in Markov decision processes (MDPs), which can be combined easily with dynamic programming methods for policy optimisation and value estimation. This…

In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not…

We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic…

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…

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 presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) framework for the problem of learning an unknown functional dependency between a structured input space and a structured output space. Our formulation…

For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…

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,…

Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…

We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Approximating the optimal value function $v^*$ for infinite-horizon, nonlinear, autonomous optimal control problems is both challenging and essential for synthesizing real-time optimal feedback. We develop an abstract optimal recovery…