Related papers: Stability of Multi-Task Kernel Regression Algorith…
An asymptotic theory is established for linear functionals of the predictive function given by kernel ridge regression, when the reproducing kernel Hilbert space is equivalent to a Sobolev space. The theory covers a wide variety of linear…
We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…
We study theoretical properties of a broad class of regularized algorithms with vector-valued output. These spectral algorithms include kernel ridge regression, kernel principal component regression, various implementations of gradient…
This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data. The present work is a contribution towards a deeper understanding of how RNNs process input signals using the response…
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…
Key to multitask learning is exploiting relationships between different tasks to improve prediction performance. If the relations are linear, regularization approaches can be used successfully. However, in practice assuming the tasks to be…
Numerically efficient and stable algorithms are essential for kernel-based regularized system identification. The state of art algorithms exploit the semiseparable structure of the kernel and are based on the generator representation of the…
In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel…
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular,…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
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…
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…
The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous…
We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an…