arXiv research

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…

Paper calculates KL divergence for isotropic Gaussian-Markov fields.

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

Deep GMRFs improve spatial data modeling and prediction.

New method speeds up sampling of Markov random fields.

In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in $O(n)$-time, where $n$ is the number of pixels in a given image. From the persp…

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

Banded matrices can be used as precision matrices in several models including linear state-space models, some Gaussian processes, and Gaussian Markov random fields. The aim of the paper is to make modern inference methods (such as variational inference or gradient-based sampling) available for Gaussian models with band…

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associ…

Efficiently infers gene regulatory networks from spatial data.

In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted l1-norm (SL1) regularization. A Gaussian MRF is an acyclic graph representing a multivariate Gaussian distribution, where nodes are…

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

Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…

In this paper, we model the dependencies among the items that are recommended to a user in a collaborative-filtering problem via a Gaussian Markov Random Field (MRF). We build upon Besag's auto-normal parameterization and pseudo-likelihood, which not only enables computationally efficient learning, but also connects th…

A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard inference techniques to sample from the posterior, such as Markov chain Monte Carlo (…

New research shows how preconditioning can solve sparse linear regression problems efficiently.

Proposes a new method for estimating sparse precision matrices in GMRF-MM models.

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretatio…

Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse covariance matrix. We utilize a novel projected gradient method, which is faster …

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the…

Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms based on variational Gaussian (VG) approximations are widely employed since they str…

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. The benchmark information-theoretic results in the case of d-regular graphs require the number of samples to be at least proportional to the logarithm of the number of vertices to allow consistent graph recovery. When…

In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes…

We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing framework shifts towards capturing the full posterior distribution on the latent variab…

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…

Study reveals supply chain correlations in firm growth rates.

Proposes an INLA-based method for state and parameter estimation in nonlinear systems.

Bayesian imaging methods deliver trustworthy probabilities in some cases but struggle with uncertainty quantification.

Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.

We report an exact likelihood computation for Linear Gaussian Markov processes that is more scalable than existing algorithms for complex models and sparsely sampled signals. Better scaling is achieved through elimination of repeated computations in the Kalman likelihood, and by using the diagonalized form of the state…

Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementatio…

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two no…

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, we introduce the notion of spatially stationary distributions over geometric grap…

Given i.i.d. observations of a random vector $X \in \mathbb{R}^p$, we study the problem of estimating both its covariance matrix $Σ^*$, and its inverse covariance or concentration matrix {$Θ^* = (Σ^*)^{-1}$.} We estimate $Θ^*$ by minimizing an $\ell_1$-penalized log-determinant Bregman divergence; in the multivariate G…

The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.

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…

Study on Gaussian random fields' singularities on manifolds.

Develops a new model for cross-currency derivatives pricing.

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.