Related papers: Kernel Methods are Competitive for Operator Learni…
In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we…
In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…
Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approximation framework, the input is a function $u\in C(K_1)$…
Generative adversarial networks (GANs) are designed with the help of min-max optimization problems that are solved with stochastic gradient-type algorithms which are known to be non-robust. In this work we revisit a non-adversarial method…
This paper considers the design of nonlinear data-enabled predictive control (DeePC) using kernel functions. Compared with existing methods that use kernels to parameterize multi-step predictors for nonlinear DeePC, we adopt a novel,…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned…
Pairwise learning usually refers to a learning task which involves a loss function depending on pairs of examples, among which most notable ones include ranking, metric learning and AUC maximization. In this paper, we study an online…
One of the major breakthroughs in deep learning over the past five years has been the Generative Adversarial Network (GAN), a neural network-based generative model which aims to mimic some underlying distribution given a dataset of samples.…
We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number…
The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral…
Higher-order learning is fundamentally rooted in exploiting compositional features. It clearly hinges on enriching the representation by more elaborate interactions of the data which, in turn, tends to increase the model complexity of…
Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…
Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…
We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical solvers incur significant computational costs to respect…
Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…
We propose a new decentralized robust kernel-based learning algorithm within the framework of reproducing kernel Hilbert spaces (RKHSs) by utilizing a networked system that can be represented as a connected graph. The robust loss function…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…