Related papers: Kernel machines with two layers and multiple kerne…

How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96%, while other methods, especially kernel methods, fall relatively behind? Can we more provide theoretical justifications for this gap?…

Kernel segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. In general, it is formulated as a discrete optimization problem with combinatorial constraints. A…

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…

Kernel methods have proven to be powerful techniques for pattern analysis and machine learning (ML) in a variety of domains. However, many of their original or advanced implementations remain in Matlab. With the incredible rise and adoption…

In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor…

Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They…

Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…

This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori…

Despite the recent progress towards efficient multiple kernel learning (MKL), the structured output case remains an open research front. Current approaches involve repeatedly solving a batch learning problem, which makes them inadequate for…

Object Categorization is a challenging problem, especially when the images have clutter background, occlusions or different lighting conditions. In the past, many descriptors have been proposed which aid object categorization even in such…

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^\alpha)$ disjoint subsets. On each subset, some…

Restricted kernel machines (RKMs) represent a versatile and powerful framework within the kernel machine family, leveraging conjugate feature duality to address a wide range of machine learning tasks, including classification, regression,…

We consider the problem of learning functions within the $\mathcal{F}_{p,\pi}$ and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer neural networks, as well as kernel methods. Leveraging tools…

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the…

We consider the problem of learning an unknown function $f_{\star}$ on the $d$-dimensional sphere with respect to the square loss, given i.i.d. samples $\{(y_i,{\boldsymbol x}_i)\}_{i\le n}$ where ${\boldsymbol x}_i$ is a feature vector…

We consider optimizing two-layer neural networks in the mean-field regime where the learning dynamics of network weights can be approximated by the evolution in the space of probability measures over the weight parameters associated with…

The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate…

Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…