Related papers: Gaussian Whittle-Mat\'ern fields on metric graphs
We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different Riemann-Cartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant…
A broad class of stochastic volatility models are defined by systems of stochastic differential equations. While these models have seen widespread success in domains such as finance and statistical climatology, they typically lack an…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to…
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables.…
We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain…
In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…
We introduce a new class of nonstationary kernels, which we derive as covariance functions of a novel family of stochastic processes we refer to as string Gaussian processes (string GPs). We construct string GPs to allow for multiple types…
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex…
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
We introduce a class of random graph processes, which we call flip processes. Each such process is given by a rule which is a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labeled $k$-vertex graphs into itself ($k$…
A suitable extra differential on graph complexes can lead to a pairing of its cohomological classes. Many such extra differentials are known for various graph complexes, including Kontsevich's graph complex $GC_n$ for odd $n$. In this paper…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs…