arXiv research

New tree-structured Markov fields with Poisson marginals for counting variables.

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

Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in th…

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.

Develops a new model for cross-currency derivatives pricing.

New method speeds up sampling of Markov random fields.

Paper calculates KL divergence for isotropic Gaussian-Markov fields.

Study of cosmic microwave background polarization using spin random fields.

Existence of strong randomized equilibria in mean-field games with common noise.

New framework models neural systems with random architecture on manifolds.

The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary pot…

New method calculates geodesic distances in Gaussian random field manifolds.

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

Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched a…

Random Fourier features model reconstructs wind fields from sparse measurements.

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

The paper characterizes the geometry and topology of spin random fields.

DiAL uses Bayesian Dirichlet random fields for active learning with sparse labels.

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…

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

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

Study a risk model with tree-structured Poisson-Markov random field for rainfall events.

Reconstructing signature features from randomized vector fields in differential equations.

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…

Study on the smoothness of solutions to a specific type of stochastic differential equation.

New test detects sparse alternatives in Gaussian random fields.

The dominant language models (LMs) such as n-gram and neural network (NN) models represent sentence probabilities in terms of conditionals. In contrast, a new trans-dimensional random field (TRF) LM has been recently introduced to show superior performances, where the whole sentence is modeled as a random field. In thi…

Enhances GNN robustness during inference using Conditional Random Fields.

The paper develops methods for high-dimensional inference in Markov random fields.

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

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

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

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

Logistic regression for brain imaging without p-values.

Formula for critical points of chi fields on manifolds.

Estimates binary labels from dependent data using Markov Random Fields.

Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.

In this note, we consider a fixed vector field $V$ on $S^2$ and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where $V$ is also tangent. We show that the expected value of the corresponding counting function is asymptotic to the eigenvalue with a leading coefficient that i…

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 …

Bayesian method selects interacting regions in Markov models.

Investigates multifractal scaling in critical dynamics of random surfaces.

Study Nash equilibrium in mean field portfolio games with random market parameters.

We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…

Study loop corrections in random feature models affecting training and test errors.

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…

We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test based algorithm for learning the underlying graph structure. The novel maximization …