Article
Mathematics, Applied
Juan Baz, Pedro Alonso, Juan Manuel Pena, Raul Perez-Fernandez
Summary: This paper focuses on the conditions for the covariance matrix of a multivariate Gaussian distribution to be totally positive, with a particular emphasis on Gaussian Markov Random Fields. It is proven that if the graph representing the Gaussian Markov Random Field consists of path graphs and the covariances between adjacent variables are non-negative, then a reordering of the variables can be found to make the resulting covariance matrix totally positive. The paper also identifies this reordering and provides some necessary and sufficient conditions for the covariance matrix of a multivariate Gaussian distribution to be totally positive.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Information Systems
Hongjun Li, Miguel Barao, Luis Rato, Shengjun Wen
Summary: This paper focuses on the mapping problem for mobile robots in dynamic environments, using a Markov chain and Gaussian random fields to model the dynamic behavior of points and capture spatial correlation. The proposed method allows for learning unobserved space and provides a map that describes occupancy probabilities and dynamics.
Review
Physics, Multidisciplinary
Enrique Hernandez-Lemus
Summary: A random field represents the joint probability distribution of a set of random variables, with Markov fields serving as the theoretical foundation for many applications in statistical physics and probability. While Markov random fields have been used in statistical physics for a long time, their measure theoretical foundations were developed later on. Besides theoretical relevance, Markov random fields have been widely used in various fields like computational molecular biology, ecology and computer vision.
FRONTIERS IN PHYSICS
(2021)
Article
Statistics & Probability
Hee Cheol Chung, Irina Gaynanova, Yang Ni
Summary: Microorganisms play critical roles in host health. We propose a novel Bayesian graphical model that incorporates evolutionary history and zero inflation to quantify microbial counts using the latest microbiome profiling technique. Through simulation studies and analysis of real data, we find that this model offers higher accuracy in estimating microbial interaction networks.
ANNALS OF APPLIED STATISTICS
(2022)
Article
Computer Science, Artificial Intelligence
Wangxiang Ding, Wenzhong Li, Zhijie Zhang, Chen Wan, Jianhui Duan, Sanglu Lu
Summary: This article proposes a novel clustering approach for multivariate time series (MTS) data based on time-varying features. It introduces a time-varying Gaussian Markov Random Fields (T-GMRF) model to capture the correlation structure between MTS variables and formulates the feature extraction problem as a convex optimization problem. The proposed method outperforms existing techniques on various clustering performance metrics, as demonstrated through extensive experiments on 33 open MTS datasets.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
(2023)
Article
Mathematics, Applied
Juan Baz, Pedro Alonso, Raill Perez-Fernandez
Summary: This paper addresses the matrix construction problem of Gaussian Markov Random Fields with uniform correlation. It provides a characterization of the correlation matrix for a Gaussian Markov Random Field with uniform correlation over a cycle graph, which is circulant and has a sparse inverse matrix. The relationship with the stationary Gaussian Markov Process on the circle is also studied, and two methods for computing the correlation matrix are provided. Asymptotic results for cycle graphs of large order reveal the connection between Gaussian Markov Random Fields with uniform correlation over cycle and path graphs.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Review
Engineering, Civil
Aditya Pandey, Ashmeet Singh, Paolo Gardoni
Summary: This paper reviews the diagrammatic perturbation theory, a technique in Information Field Theory, for analytically estimating moments of perturbative non-Gaussian distributions. When dealing with physical phenomena, which often exhibit non-Gaussian features, approximation of the underlying distribution and inference of its parameter form are commonly used. More rigorous analysis methods such as Markov Chain Monte Carlo can also be employed, but are computationally expensive.
Article
Automation & Control Systems
Yang Ni, Francesco C. Stingo, Veerabhadran Baladandayuthapani
Summary: We introduce Bayesian Gaussian graphical models with covariates (GGMx), which are multivariate Gaussian distributions with covariate-dependent sparse precision matrix. We propose a general construction that maps the covariate space to sparse positive definite matrices, allowing for changes in strength and sparsity pattern of the precision matrix (graph structure) with the covariates. Our approach utilizes a novel mixture prior for precision matrices and ensures positive definiteness of sparse precision matrices using a carefully designed Markov chain Monte Carlo algorithm. Extensive simulations and a case study in cancer genomics demonstrate the utility of the proposed model.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Mathematics
Kausthub Keshava, Alain Jean-Marie, Sara Alouf
Summary: This study proposes a model for optimizing document prefetching, where a random surfer moves along a random tree with the controller only knowing the tree up to a certain depth. The model was analyzed using Markov decision process theory to determine the optimal policy for minimizing the probability of the surfer moving to a node not prefetched.
Article
Statistics & Probability
Daniel Sanz-Alonso, Ruiyi Yang
Summary: This paper investigates the Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations, establishing approximation error guarantees based on the theory of spectral convergence of graph Laplacians. The proposed graph representations generalize the Matern model to unstructured point clouds and enable inference and sampling using linear algebra methods for sparse matrices. Moreover, they bridge and unify several models in Bayesian inverse problems, spatial statistics, and graph-based machine learning, demonstrating the benefits of exchanging ideas across these disciplines.
STATISTICAL SCIENCE
(2022)
Article
Computer Science, Artificial Intelligence
Muhammad Hameed Siddiqi
Summary: This study focuses on improving the emotional speech classifier by introducing a novel methodology to address the limitations of existing classifiers, achieving significant improvement in emotional recognition. The proposed method has been validated and evaluated on two datasets, showing significantly improved classification performance. In terms of computation, the technique is also more cost-effective compared to state of the art works.
EGYPTIAN INFORMATICS JOURNAL
(2021)
Article
Geosciences, Multidisciplinary
Finn Lindgren, David Bolin, Havard Rue
Summary: This article provides an overview of Gaussian processes and random fields, their history, and various approaches to representing spatial and spatiotemporal dependence structures. The connection between stochastic partial differential equation approach and Matern covariance models is explained, along with important extensions, theory, applications, and recent developments.
SPATIAL STATISTICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Alexandre L. M. Levada
Summary: This paper proposes an information-geometric framework to analyze Gaussian-Markov random fields (GMRF's) and measures the variations in the metric tensor components to understand the changes in the system over time. A method based on infinitesimal displacements using Markov Chain Monte Carlo simulations is used to compute distances between two systems operating in different regimes using the Fisher metric. Additionally, an expression for the KL-divergence between two GMRF models is derived, showing that it can be a good replacement for the Fisher information based distance. Moreover, the paper reveals an asymmetric pattern of evolution when the system moves towards different entropic states, indicating the emergence of an intrinsic notion of time based on the geometric properties of its parametric space.
JOURNAL OF COMPUTATIONAL SCIENCE
(2022)
Article
Geosciences, Multidisciplinary
Martin Outzen Berild, Geir-Arne Fuglstad
Summary: Isotropic covariance structures may not be appropriate for phenomena in three-dimensional spaces. We propose a non-stationary anisotropic Gaussian random fields (GRFs) model in three dimensions using stochastic partial differential equations (SPDEs), with efficient computations based on Gaussian Markov random field approximations. The unique aspect of our model lies in the parameterization of spatially varying anisotropy through vector fields.
SPATIAL STATISTICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Hugo Gangloff, Jean-Baptiste Courbot, Emmanuel Monfrini, Christophe Collet
Summary: The Gaussian Pairwise Markov Field model is introduced to generalize existing latent variable models and introduce more correlations between variables. This new model offers a generalization of classical Markov Field modelization.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2021)
Article
Statistics & Probability
Elchanan Mussel, Joe Neeman
ANNALS OF PROBABILITY
(2015)
Article
Mathematics, Applied
Elchanan Mossel, Joe Neeman
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2015)
Article
Ecology
Junhyong Kim, Elchanan Mossel, Miklos Z. Racz, Nathan Ross
THEORETICAL POPULATION BIOLOGY
(2015)
Article
Mathematics
Elchanan Mossel, Miklos Z. Racz
Article
Statistics & Probability
Jian Ding, Elchanan Mossel
ELECTRONIC COMMUNICATIONS IN PROBABILITY
(2014)
Article
Computer Science, Information Systems
Siu On Chan, Elchanan Mossel, Joe Neeman
IEEE TRANSACTIONS ON INFORMATION THEORY
(2014)
Letter
Biology
Elchanan Mossel, Mike Steel
JOURNAL OF THEORETICAL BIOLOGY
(2014)
Article
Statistics & Probability
Elchanan Mossel, Allan Sly, Omer Tamuz
PROBABILITY THEORY AND RELATED FIELDS
(2014)
Article
Statistics & Probability
Elchanan Mossel, Joe Neeman, Allan Sly
PROBABILITY THEORY AND RELATED FIELDS
(2015)
Article
Physics, Multidisciplinary
Elchanan Mossel, Mesrob I. Ohannessian
Article
Statistics & Probability
Yuval Filmus, Elchanan Mossel
PROBABILITY THEORY AND RELATED FIELDS
(2019)
Article
Management
Dean Eckles, Hossein Esfandiari, Elchanan Mossel, M. Amin Rahimian
Summary: In this study, the task of selecting k nodes in a social network to maximize the expected spread size of a diffusion is examined. The authors propose algorithms and guarantees to approximate the optimal seed set while limiting the amount of collected network information. They investigate the achievable guarantees using a sublinear influence sample size and develop a probing algorithm to find the seed set with the same approximation guarantee.
OPERATIONS RESEARCH
(2022)
Article
Computer Science, Information Systems
Anuran Makur, Elchanan Mossel, Yury Polyanskiy
Summary: This paper studies the problem of broadcasting on two-dimensional regular grids, which is a specialization of the general broadcasting problem on directed acyclic graphs. The authors make progress towards establishing the conjecture that it is impossible to propagate information in a 2D regular grid regardless of the noise level and the choice of processing function. They prove that recovery of the source vertex X is impossible for any noise level between 0 and 1/2 when all vertices with indegree 2 use either AND or XOR for their processing functions.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Automation & Control Systems
Ali Jadbabaie, Anuran Makur, Elchanan Mossel, Rabih Salhab
Summary: This article presents a new opinion dynamics model in which a group of agents hold inherent and declared opinions. The agents' inherent opinions are fixed and cannot be observed by others. At each time step, agents share their declared opinions on a social network based on their inherent opinions and social pressure. The paper investigates the possibility of estimating agents' inherent opinions from their declared opinions, using the example of predicting election results based on voters' tweets. The analysis shows that estimation of aggregate and individual inherent opinions is possible unless there are large majorities, which cause minorities to lie over time, making asymptotic estimation impossible.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Engineering, Multidisciplinary
Sebastien Bubeck, Elchanan Mossel, Miklos Z. Racz
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2015)