Related papers: An Online Stochastic Kernel Machine for Robust Sig…
We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
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…
We consider multi-agent stochastic optimization problems over reproducing kernel Hilbert spaces (RKHS). In this setting, a network of interconnected agents aims to learn decision functions, i.e., nonlinear statistical models, that are…
An adaptive observer is designed for online estimation of Hilbert-Schmidt operators from online measurement of the state for some class of nonlinear infinite-dimensional dynamical systems. Convergence is ensured under detectability and…
We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…
In this paper, an online learning algorithm is proposed as sequential stochastic approximation of a regularization path converging to the regression function in reproducing kernel Hilbert spaces (RKHSs). We show that it is possible to…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…
This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional…
This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
In this paper, sparsification techniques aided online prediction algorithms in a reproducing kernel Hilbert space are studied for nonstationary time series. The online prediction algorithms as usual consist of the selection of kernel…
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
We discuss how to define a kernel for Signal Temporal Logic (STL) formulae. Such a kernel allows us to embed the space of formulae into a Hilbert space, and opens up the use of kernel-based machine learning algorithms in the context of STL.…
We develop a non-parametric, data-driven, tractable approach for solving multistage stochastic optimization problems in which decisions do not affect the uncertainty. The proposed framework represents the decision variables as elements of a…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…