Related papers: Gaussian Whittle-Mat\'ern fields on metric graphs

The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial…

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

In a series of publications we developed "differential geometry" on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first order differential calculi (over the algebra of functions) on a discrete…

We study the filtering and smoothing problem for continuous-time linear Gaussian systems. While classical approaches such as the Kalman-Bucy filter and the Rauch-Tung-Striebel (RTS) smoother provide recursive formulas for the conditional…

Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`{e}ve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of…

We study estimation and prediction of Gaussian processes with covariance model belonging to the generalized Cauchy (GC) family, under fixed domain asymptotics. Gaussian processes with this kind of covariance function provide separate…

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that…

We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function. The key property of differential Gaussian…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

We present a novel way of constructing the Gaussian Free Field on a weighted graph via a dynamical expansion of the Green function along an expanding family of subgraphs. Along the way we obtain the discrete analogue of the classical…

We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U of M, based on the geometric and extensor calculus on an…

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…

Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…

Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated…

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…