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Optimal frequency identification in astronomical datasets is crucial for variable star studies, exoplanet detection, and asteroseismology. Traditional period-finding methods often rely on specific parametric assumptions, employ binning…
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like…
We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix…
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time…
In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…
Contemporary deep neural networks exhibit impressive results on practical problems. These networks generalize well although their inherent capacity may extend significantly beyond the number of training examples. We analyze this behavior in…
We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…
We introduce a novel topology, called Kernel Mean Embedding Topology, for stochastic kernels, in a weak and strong form. This topology, defined on the spaces of Bochner integrable functions from a signal space to a space of probability…
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
Gaussian Processes (GPs) are a versatile method that enables different approaches towards learning for dynamics and control. Gaussianity assumptions appear in two dimensions in GPs: The positive semi-definite kernel of the underlying…
We describe an application of machine learning to the problem of predicting preterm birth. We conduct a secondary analysis on a clinical trial dataset collected by the National In- stitute of Child Health and Human Development (NICHD) while…
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…
Among various quantum machine learning (QML) algorithms, the quantum kernel method has especially attracted attention due to its compatibility with noisy intermediate-scale quantum devices and its potential to achieve quantum advantage.…
We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set $X$, generalizing Loewner, we make precise the corresponding partially ordered…