Probabilistic Context Neighborhood model for lattices

Duarte, Denise; Magalhães, Débora F.; Piroutek, Aline M.; Alves, Caio

doi:10.1016/j.spasta.2024.100830

Title: Probabilistic Context Neighborhood model for lattices

Journal Article · 13 April 2024 · Spatial Statistics

DOI: https://doi.org/10.1016/j.spasta.2024.100830 · OSTI ID:2429789

^[1]; Magalhães, Débora F. ^[1]; Piroutek, Aline M. ^[1];

^[2]

Universidade Federal de Minas Gerais (UFMG) (Brazil)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Here we present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov random field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable order, depending on the neighbors’ values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependence neighborhood structure as a graph in a tree format, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2429789

Journal Information:: Spatial Statistics, Journal Name: Spatial Statistics Vol. 61; ISSN 2211-6753

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (24)

Markov approximation and consistent estimation of unbounded probabilistic suffix trees Duarte, Denise; Galves, Antonio; Garcia, Nancy L. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 37, Issue 4 https://doi.org/10.1007/s00574-006-0029-7	journal	December 2006
Modeling Economic Activities and Random Catastrophic Failures of Financial Networks via Gibbs Random Fields Onural, Levent; Pınar, Mustafa Çelebi; Fırtına, Can Computational Economics, Vol. 58, Issue 2 https://doi.org/10.1007/s10614-020-10023-3	journal	August 2020
An integrated approach for scene understanding based on Markov Random Field model Kim, Il Y.; Yang, Hyun S. Pattern Recognition, Vol. 28, Issue 12 https://doi.org/10.1016/0031-3203(95)00061-5	journal	December 1995
Spatio-contextual fuzzy clustering with Markov random field model for change detection in remotely sensed images Subudhi, Badri Narayan; Bovolo, Francesca; Ghosh, Ashish Optics & Laser Technology, Vol. 57 https://doi.org/10.1016/j.optlastec.2013.10.003	journal	April 2014
Neighborhood radius estimation for variable-neighborhood random fields Löcherbach, Eva; Orlandi, Enza Stochastic Processes and their Applications, Vol. 121, Issue 9 https://doi.org/10.1016/j.spa.2011.05.001	journal	September 2011
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
Markov Graphs Frank, Ove; Strauss, David Journal of the American Statistical Association, Vol. 81, Issue 395 https://doi.org/10.1080/01621459.1986.10478342	journal	September 1986
Variations on probabilistic suffix trees: statistical modeling and prediction of protein families Bejerano, Gill; Yona, Golan Bioinformatics, Vol. 17, Issue 1 https://doi.org/10.1093/bioinformatics/17.1.23	journal	January 2001
A Markov random field model for network-based analysis of genomic data Wei, Zhi; Li, Hongzhe Bioinformatics, Vol. 23, Issue 12 https://doi.org/10.1093/bioinformatics/btm129	journal	May 2007
Monte Carlo sampling methods using Markov chains and their applications Hastings, W. K. Biometrika, Vol. 57, Issue 1 https://doi.org/10.1093/biomet/57.1.97	journal	April 1970
The context-tree weighting method: basic properties Willems, F. M. J.; Shtarkov, Y. M.; Tjalkens, T. J. IEEE Transactions on Information Theory, Vol. 41, Issue 3 https://doi.org/10.1109/18.382012	journal	May 1995
A universal data compression system Rissanen, J. IEEE Transactions on Information Theory, Vol. 29, Issue 5 https://doi.org/10.1109/TIT.1983.1056741	journal	September 1983
Linear Time Universal Coding and Time Reversal of Tree Sources Via FSM Closure Martin, A.; Seroussi, G.; Weinberger, M. J. IEEE Transactions on Information Theory, Vol. 50, Issue 7 https://doi.org/10.1109/TIT.2004.830763	journal	July 2004
Context tree estimation for not necessarily finite memory processes, via BIC and MDL Csiszar, I.; Talata, Z. IEEE Transactions on Information Theory, Vol. 52, Issue 3 https://doi.org/10.1109/TIT.2005.864431	journal	March 2006
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images Geman, Stuart; Geman, Donald IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-6, Issue 6 https://doi.org/10.1109/TPAMI.1984.4767596	journal	November 1984
Markov Random Fields with Higher-order Interactions Tjelmeland, Hakon; Besag, Julian Scandinavian Journal of Statistics, Vol. 25, Issue 3 https://doi.org/10.1111/1467-9469.00113	journal	September 1998
Consistent estimation of the basic neighborhood of Markov random fields Csiszár, Imre; Talata, Zsolt The Annals of Statistics, Vol. 34, Issue 1 https://doi.org/10.1214/009053605000000912	journal	February 2006
Testing statistical hypothesis on random trees and applications to the protein classification problem Busch, Jorge R.; Ferrari, Pablo A.; Flesia, Ana Georgina The Annals of Applied Statistics, Vol. 3, Issue 2 https://doi.org/10.1214/08-AOAS218	journal	June 2009
Context tree selection and linguistic rhythm retrieval from written texts Galves, Antonio; Galves, Charlotte; García, Jesús E. The Annals of Applied Statistics, Vol. 6, Issue 1 https://doi.org/10.1214/11-AOAS511	journal	March 2012
A Markov random field-based approach to characterizing human brain development using spatial–temporal transcriptome data Lin, Zhixiang; Sanders, Stephan J.; Li, Mingfeng The Annals of Applied Statistics, Vol. 9, Issue 1 https://doi.org/10.1214/14-AOAS802	journal	March 2015
Marginal Pseudo-Likelihood Learning of Discrete Markov Network Structures Pensar, Johan; Nyman, Henrik; Niiranen, Juha Bayesian Analysis, Vol. 12, Issue 4 https://doi.org/10.1214/16-BA1032	journal	December 2017
A consistent model selection procedure for Markov random fields based on penalized pseudolikelihood Ji, Chuanshu; Seymour, Lynne The Annals of Applied Probability, Vol. 6, Issue 2 https://doi.org/10.1214/aoap/1034968138	journal	May 1996
Variable length Markov chains Bühlmann, Peter; Wyner, Abraham J. The Annals of Statistics, Vol. 27, Issue 2 https://doi.org/10.1214/aos/1018031204	journal	April 1999
Random Fields in Physics, Biology and Data Science Hernández-Lemus, Enrique Frontiers in Physics, Vol. 9 https://doi.org/10.3389/fphy.2021.641859	journal	April 2021

Similar Records

Searching for planning operators with context-dependent and probabilistic effects

Conference · 1996 · OSTI ID:430754

Oates, T; Cohen, P R

New probabilistic modeling and simulation methods for complex time-dependent systems

Conference · 1985 · OSTI ID:5506098

Bartholomew, R J

Distributed coloration neighborhood search

Conference · 1994 · OSTI ID:36304

Morgenstern, C

Related Subjects

97 MATHEMATICS AND COMPUTING
Context algorithm
Markov random fields
Model selection
Probabilistic context trees
Pseudo-Bayesian information criterion
Variable-neighborhood random fields

Title: Probabilistic Context Neighborhood model for lattices

Citation Formats

References (24)

Similar Records

Related Subjects