Related papers: Regular Fourier Features for Nonstationary Gaussia…
The second in a two-part series, this paper extends the 3rd-order Spectral Representation Method for simulation of ergodic multi-variate stochastic processes according to a prescribed cross power spectral density and cross bispectral…
Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
Sup-normalized spectral functions form building blocks of max-stable and Pareto processes and therefore play an important role in modeling spatial extremes. For one of the most popular examples, the Brown-Resnick process, simulation is not…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
Despite more than 40 years of research in condensed-matter physics, state-of-the-art approaches for simulating the radial distribution function (RDF) g(r) still rely on binning pair-separations into a histogram. Such methods suffer from…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…
Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
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…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
Numerical relativity (NR) enables the study of physics in strong and dynamical gravitational fields and provides predictions for the gravitational-wave signals produced by merging black holes. Despite the impressive accuracy of modern…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…