arXiv research

CMRFs extend PGMs for topological data, capturing both conditional and marginal dependencies.

New method calculates geodesic distances in Gaussian random field manifolds.

HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.

New test detects sparse alternatives in Gaussian random fields.

Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, calle…

Study on Gaussian random fields' singularities on manifolds.

Research proves the semi-classical limit of Liouville conformal field theory, describing deterministic geometry from random fluctuations.

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary c…

The paper proves that Gaussian field critical points have finite moments.

Paper calculates KL divergence for isotropic Gaussian-Markov fields.

New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.

New method controls false discovery rate in learning Gaussian MRF structures.

Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.

We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian random field. In this setting, the posterior distribution on the objective func…

Bounds on Gaussian approximation for neural networks with novel smoothing techniques.

In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give constructions for kernels. Finally we present e cient means of solving the optimization…

For highly sensitive real-world predictive analytic applications such as healthcare and medicine, having good prediction accuracy alone is often not enough. These kinds of applications require a decision making process which uses uncertainty estimation as input whenever possible. Quality of uncertainty estimation is a …

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 labels is given by a type of conditional Markov random field. In the supervised…

Motivated by numerous questions in random geometry, given a smooth manifold $M$, we approach a systematic study of the differential topology of Gaussian random fields (GRF) $X:M\to \mathbb{R}^k$, that we interpret as random variables with values in $\mathcal{C}^r(M, \mathbb{R}^k)$, inducing on it a Gaussian measure. Wh…

The paper develops a uniform function estimator in RKHS for regression.

Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which is provided by a similarity measure. In this paper, a Gaussian conditional rando…

Study of cosmic microwave background polarization using spin random fields.

This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on Metropolis-Hastings algorithm. Next, by using MH algorithm, we simulate the data from Ising model…

Study on spin random fields using chaos decomposition for cosmic microwave background modeling.

To improve the classification performance in the context of hyperspectral image processing, many works have been developed based on two common strategies, namely the spatial-spectral information integration and the utilization of neural networks. However, both strategies typically require more training data than the cl…

New method speeds up sampling of Markov random fields.

We adapt a Markov Random Field learning algorithm for continuous variables.

In this paper we model the loss function of high-dimensional optimization problems by a Gaussian random field, or equivalently a Gaussian process. Our aim is to study gradient descent in such loss functions or energy landscapes and compare it to results obtained from real high-dimensional optimization problems such as …

A new method uses SPDEs to efficiently model random fields on complex domains.

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via…

This is supplementary material for the main Geodesics article by the authors. In Appendix A, we present some general results on the construction of Gaussian random fields. In Appendix B, we restate our Shape Theorem, specialized to the setting of this article. In Appendix C, we state some straightforward consequences o…

Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf \mathbf{M}}$, and a constant $-1 \leq p \leq 1$, our algorithm gives efficient access to a…

We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended…

Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.

BEGIN network models binary data without parametric assumptions.

Study finds Calabi-Yau models' operator spectra match random matrix theory.

New framework models neural systems with random architecture on manifolds.

A scalable deep GMRF model for general graphs improves predictions and uncertainty estimates.

Bayesian DOE accelerates experimental design with improved efficiency.

This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean vector, and message passing between neighbors. Under broad conditions, it is show…

In this work we introduce a time- and memory-efficient method for structured prediction that couples neuron decisions across both space at time. We show that we are able to perform exact and efficient inference on a densely connected spatio-temporal graph by capitalizing on recent advances on deep Gaussian Conditional …

Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the evaluation of the Cholesky factorization or solving linear systems. Recently, Anit…

Deep GMRFs improve spatial data modeling and prediction.

Characterizes nodal volumes of Gaussian fields on manifolds, extending previous work.

We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of…

Consider a random smooth Gaussian field $G(x):F\to\mathbb{R}$, where $F$ is a compact in $\mathbb{R}^d$. We derive a formula for average area of a surface generated by the equation $G(x)=0$ and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of a \e…

We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF models. Theoretical convergence rates for the estimated between-response covariance…

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-sca…