Related papers: Kernel Flows: from learning kernels from data into…

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…

In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory…

Recent empirical work has shown that hierarchical convolutional kernels inspired by convolutional neural networks (CNNs) significantly improve the performance of kernel methods in image classification tasks. A widely accepted explanation…

Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…

Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…

We propose a novel family of connectionist models based on kernel machines and consider the problem of learning layer-by-layer a compositional hypothesis class, i.e., a feedforward, multilayer architecture, in a supervised setting. In terms…

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…

Kernel estimation is generally one of the key problems for blind image super-resolution (SR). Recently, Double-DIP proposes to model the kernel via a network architecture prior, while KernelGAN employs the deep linear network and several…

Machine Learning (ML) and Algorithmic Information Theory (AIT) look at Complexity from different points of view. We explore the interface between AIT and Kernel Methods (that are prevalent in ML) by adopting an AIT perspective on the…

In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…

Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…

As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a…

In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…