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Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
The first part of this work considers a general class of covariance estimators. Each estimator of that class is generated by a real-valued function $g$ and a set of model covariance matrices $H$. If $\bf{W}$ is a potentially perturbed…
Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…
Generative models dealing with modeling a~joint data distribution are generally either autoencoder or GAN based. Both have their pros and cons, generating blurry images or being unstable in training or prone to mode collapse phenomenon,…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or…
In this article a surprising result is demonstrated using the neural tangent kernel. This kernel is defined as the inner product of the vector of the gradient of an underlying model evaluated at training points. This kernel is used to…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
Spectral risk measures (SRMs) belong to the family of coherent risk measures. A natural estimator for the class of SRMs has the form of L-statistics. Various authors have studied and derived the asymptotic properties of the empirical…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
Convolutional neural networks (CNNs) have become widely adopted in gravitational wave (GW) detection pipelines due to their ability to automatically learn hierarchical features from raw strain data. However, the physical meaning of these…
We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…
This paper studies random operator-valued positive definite (p.d.) kernels and their connection to moment dilations. A class of random p.d. kernels is introduced in which the positivity requirement is imposed only in expectation, extending…
Interest in generative models has grown tremendously in the past decade. However, their training performance can be adversely affected by contamination, where outliers are encoded in the representation of the model. This results in the…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It…