Related papers: Online Pairwise Learning Algorithms with Kernels
Learning with Reproducing Kernel Hilbert Spaces (RKHS) has been widely used in many scientific disciplines. Because a RKHS can be very flexible, it is common to impose a regularization term in the optimization to prevent overfitting.…
Pair-wise loss is an approach to metric learning that learns a semantic embedding by optimizing a loss function that encourages images from the same semantic class to be mapped closer than images from different classes. The literature…
Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…
Data-driven spectral analysis of Koopman operators is a powerful tool for understanding numerous real-world dynamical systems, from neuronal activity to variations in sea surface temperature. The Koopman operator acts on a function space…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the…
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary…
This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
We introduce an efficient algorithmic framework for model selection in online learning, also known as parameter-free online learning. Departing from previous work, which has focused on highly structured function classes such as nested balls…
We consider the problem of learning linear operators under squared loss between two infinite-dimensional Hilbert spaces in the online setting. We show that the class of linear operators with uniformly bounded $p$-Schatten norm is online…
Probabilistic predictions are probability distributions over the set of possible outcomes. Such predictions quantify the uncertainty in the outcome, making them essential for effective decision making. By combining multiple predictions, the…
This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly…
We propose a new supervised learning algorithm, for classification and regression problems where two or more preliminary predictors are available. We introduce \texttt{KernelCobra}, a non-linear learning strategy for combining an arbitrary…
This paper introduces a solution to the problem of selecting dynamically (online) the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the probability density function of the outliers. The proposed…
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a \textit{multiwavelet-based neural operator learning scheme}…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…