Related papers: On regularized Shannon sampling formulas with loca…

This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…

This is an overview about natural sample spaces for differential equations driven by various noises. Appropriate sample spaces are needed in order to facilitate a random dynamical systems approach for stochastic differential equations. The…

Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms.Here, we introduce…

The R package sns implements Stochastic Newton Sampler (SNS), a Metropolis-Hastings Monte Carlo Markov Chain algorithm where the proposal density function is a multivariate Gaussian based on a local, second-order Taylor series expansion of…

Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…

We present a new refinement strategy for locally refined B-splines which ensures the local linear independence of the basis functions. The strategy also guarantees the spanning of the full spline space on the underlying locally refined…

In this work we introduced a new proposal to study the gravitational lensing theory by spherical lenses, starting from its surface mass density $\Sigma(x)$ written in terms of a decreasing function $f$ of a dimensionless coordinate $x$ on…

Here we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin…

We show that regularizing Bayesian predictive regressions provides a framework for prior sensitivity analysis. We develop a procedure that jointly regularizes expectations and variance-covariance matrices using a pair of shrinkage priors.…

We present a principled approach for designing stochastic Newton methods for solving finite sum optimization problems. Our approach has two steps. First, we re-write the stationarity conditions as a system of nonlinear equations that…

In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed…

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…

We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…

Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al.,…

Normalization layers have been shown to improve convergence in deep neural networks, and even add useful inductive biases. In many vision applications the local spatial context of the features is important, but most common normalization…

In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular…

Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…