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We introduce property-independent kernels for machine learning modeling of arbitrarily many molecular properties. The kernels encode molecular structures for training sets of varying size, as well as similarity measures sufficiently diffuse…

We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a…

The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…

We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to…

Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate…

Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces…

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…

Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…

In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…

Nowadays, hyperspectral image classification widely copes with spatial information to improve accuracy. One of the most popular way to integrate such information is to extract hierarchical features from a multiscale segmentation. In the…

Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…

In this work, we investigate high-dimensional kernel ridge regression (KRR) on i.i.d. Gaussian data with anisotropic power-law covariance. This setting differs fundamentally from the classical source & capacity conditions for KRR, where…

Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…

The saturation effects, which originally refer to the fact that kernel ridge regression (KRR) fails to achieve the information-theoretical lower bound when the regression function is over-smooth, have been observed for almost 20 years and…

Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights.…

We present Neural Kernel Fields: a novel method for reconstructing implicit 3D shapes based on a learned kernel ridge regression. Our technique achieves state-of-the-art results when reconstructing 3D objects and large scenes from sparse…

Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…

A recent line of work studies overparametrized neural networks in the "kernel regime," i.e. when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the…

Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…

Deep-learning based Super-Resolution (SR) methods have exhibited promising performance under non-blind setting where blur kernel is known. However, blur kernels of Low-Resolution (LR) images in different practical applications are usually…