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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…
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently,…
We give a comprehensive self-contained review on the rigorous analysis of the thermodynamics of a class of random spin systems of mean field type whose most prominent example is the Hopfield model. We focus on the low temperature phase and…
McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over…
Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…
We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
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 Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…
Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which…
The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…
In a recent work (arXiv:2206.10724), Muirhead has studied level-set percolation of (discrete or continuous) Gaussian fields, and has shown sharpness of the associated phase transition under the assumption that the field has a certain…
The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic…
Consider ``stochastic differential equations" driven by fractional Brownian motion with Hurst parameter H (1/4 <H< 1). Their solutions are sometimes called fractional diffusion processes. The main purpose of this paper is conditioning these…
About forty years ago it was realized by several researchers that the essential features of certain objects of Probability theory, notably Gaussian processes and limit theorems, may be better understood if they are considered in settings…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…