Related papers: Extending the average spectrum method: Grid points…

In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…

Let a graph be observed through a finite random sampling mechanism. Spectral methods are routinely applied to such graphs, yet their outputs are treated as deterministic objects. This paper develops finite-sample inference for spectral…

We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…

Statistical techniques are needed to analyse data structures with complex dependencies such that clinically useful information can be extracted. Individual-specific networks, which capture dependencies in complex biological systems, are…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…

In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method…

Markov Chain Monte Carlo methods for sampling from complex distributions and estimating normalization constants often simulate samples from a sequence of intermediate distributions along an annealing path, which bridges between a tractable…

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…

This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the…

The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…

We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…

This paper deals with the state estimation of stochastic models with continuous dynamics. The aim is to incorporate spectral differentiation methods into the solution to the Fokker-Planck equation in grid-based state estimation routine,…

Dense crowd counting aims to predict thousands of human instances from an image, by calculating integrals of a density map over image pixels. Existing approaches mainly suffer from the extreme density variances. Such density pattern shift…

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…

We consider a typical learning problem of point estimations for modeling of nonlinear functions or dynamical systems in which generalization, i.e., verifying a given learned model, can be embedded as an integral part of the learning process…

This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data. We apply this technique to both synthetic and Monte Carlo-generated data. The training sets for neural networks are…

The problem of learning the structure of a high dimensional graphical model from data has received considerable attention in recent years. In many applications such as sensor networks and proteomics it is often expensive to obtain samples…

When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…

We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…