Centrality and shape-related comparisons in a tree-structured Markov random field Article Swipe

PDF

B. M. Cote , Hélène Cossette , Étienne Marceau ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2410.20240

Understanding the effects of the choice of the tree on the joint distribution of a tree-structured Markov random field (MRF) is crucial for fully exploiting the intelligibility of such probabilistic graphical models. Tools must be developed in this regard: this is the overarching objective of this paper. Our discussion is two-fold. First, we examine concepts specific to network centrality theory. We put forth a new conception of centrality for MRFs that not only accounts for the tree topology, but also the underlying stochastic dynamics. In this vein, we compare synecdochic pairs, random vectors comprising a MRF's component and its sum, using stochastic orders. The resulting orderings are transferred to risk-allocation quantities, which therefore serve as new centrality indices tailored to our stochastic framework. Second, we shed light on the influence of the tree's shapes, by establishing convex orderings for MRFs encrypted on trees of different shapes. This results in the design of a new partial order on tree shapes. This analysis is done within the framework of a propagation-based family of tree-structured MRFs with the uncommon property of having fixed Poisson marginal distributions unaffected by the dependence scheme. This work is a first step into the analysis of MRFs' trees' shapes and a stepping stone to extending this analysis to a broader framework.

Related Topics

Concepts

Centrality Markov chain Tree (set theory) Field (mathematics) Topology (electrical circuits) Computer science Mathematics Statistical physics Statistics Physics Combinatorics Pure mathematics

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2410.20240
PDF: https://arxiv.org/pdf/2410.20240
OA Status: green
Cited By: 1
Related Works: 10
OpenAlex ID: https://openalex.org/W4404313856

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4404313856

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2410.20240

Digital Object Identifier
Title: Centrality and shape-related comparisons in a tree-structured Markov random field

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2024

Year of publication
Publication date: 2024-10-26

Full publication date if available
Authors: B. M. Cote, Hélène Cossette, Étienne Marceau

List of authors in order
Landing page: https://arxiv.org/abs/2410.20240

Publisher landing page
PDF URL: https://arxiv.org/pdf/2410.20240

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2410.20240

Direct OA link when available
Concepts: Centrality, Markov chain, Tree (set theory), Field (mathematics), Topology (electrical circuits), Computer science, Mathematics, Statistical physics, Statistics, Physics, Combinatorics, Pure mathematics

Top concepts (fields/topics) attached by OpenAlex
Cited by: 1

Total citation count in OpenAlex
Citations by year (recent): 2025: 1

Per-year citation counts (last 5 years)
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4404313856
doi	https://doi.org/10.48550/arxiv.2410.20240
ids.doi	https://doi.org/10.48550/arxiv.2410.20240
ids.openalex	https://openalex.org/W4404313856
fwci
type	preprint
title	Centrality and shape-related comparisons in a tree-structured Markov random field
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10064
topics[0].field.id	https://openalex.org/fields/31
topics[0].field.display_name	Physics and Astronomy
topics[0].score	0.9592999815940857
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/3109
topics[0].subfield.display_name	Statistical and Nonlinear Physics
topics[0].display_name	Complex Network Analysis Techniques
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C53811970
concepts[0].level	2
concepts[0].score	0.8152145147323608
concepts[0].wikidata	https://www.wikidata.org/wiki/Q5062194
concepts[0].display_name	Centrality
concepts[1].id	https://openalex.org/C98763669
concepts[1].level	2
concepts[1].score	0.5563720464706421
concepts[1].wikidata	https://www.wikidata.org/wiki/Q176645
concepts[1].display_name	Markov chain
concepts[2].id	https://openalex.org/C113174947
concepts[2].level	2
concepts[2].score	0.551752507686615
concepts[2].wikidata	https://www.wikidata.org/wiki/Q2859736
concepts[2].display_name	Tree (set theory)
concepts[3].id	https://openalex.org/C9652623
concepts[3].level	2
concepts[3].score	0.5190494656562805
concepts[3].wikidata	https://www.wikidata.org/wiki/Q190109
concepts[3].display_name	Field (mathematics)
concepts[4].id	https://openalex.org/C184720557
concepts[4].level	2
concepts[4].score	0.485710471868515
concepts[4].wikidata	https://www.wikidata.org/wiki/Q7825049
concepts[4].display_name	Topology (electrical circuits)
concepts[5].id	https://openalex.org/C41008148
concepts[5].level	0
concepts[5].score	0.42446884512901306
concepts[5].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[5].display_name	Computer science
concepts[6].id	https://openalex.org/C33923547
concepts[6].level	0
concepts[6].score	0.4223887622356415
concepts[6].wikidata	https://www.wikidata.org/wiki/Q395
concepts[6].display_name	Mathematics
concepts[7].id	https://openalex.org/C121864883
concepts[7].level	1
concepts[7].score	0.3240189552307129
concepts[7].wikidata	https://www.wikidata.org/wiki/Q677916
concepts[7].display_name	Statistical physics
concepts[8].id	https://openalex.org/C105795698
concepts[8].level	1
concepts[8].score	0.19340699911117554
concepts[8].wikidata	https://www.wikidata.org/wiki/Q12483
concepts[8].display_name	Statistics
concepts[9].id	https://openalex.org/C121332964
concepts[9].level	0
concepts[9].score	0.16247475147247314
concepts[9].wikidata	https://www.wikidata.org/wiki/Q413
concepts[9].display_name	Physics
concepts[10].id	https://openalex.org/C114614502
concepts[10].level	1
concepts[10].score	0.1498548984527588
concepts[10].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[10].display_name	Combinatorics
concepts[11].id	https://openalex.org/C202444582
concepts[11].level	1
concepts[11].score	0.12373563647270203
concepts[11].wikidata	https://www.wikidata.org/wiki/Q837863
concepts[11].display_name	Pure mathematics
keywords[0].id	https://openalex.org/keywords/centrality
keywords[0].score	0.8152145147323608
keywords[0].display_name	Centrality
keywords[1].id	https://openalex.org/keywords/markov-chain
keywords[1].score	0.5563720464706421
keywords[1].display_name	Markov chain
keywords[2].id	https://openalex.org/keywords/tree
keywords[2].score	0.551752507686615
keywords[2].display_name	Tree (set theory)
keywords[3].id	https://openalex.org/keywords/field
keywords[3].score	0.5190494656562805
keywords[3].display_name	Field (mathematics)
keywords[4].id	https://openalex.org/keywords/topology
keywords[4].score	0.485710471868515
keywords[4].display_name	Topology (electrical circuits)
keywords[5].id	https://openalex.org/keywords/computer-science
keywords[5].score	0.42446884512901306
keywords[5].display_name	Computer science
keywords[6].id	https://openalex.org/keywords/mathematics
keywords[6].score	0.4223887622356415
keywords[6].display_name	Mathematics
keywords[7].id	https://openalex.org/keywords/statistical-physics
keywords[7].score	0.3240189552307129
keywords[7].display_name	Statistical physics
keywords[8].id	https://openalex.org/keywords/statistics
keywords[8].score	0.19340699911117554
keywords[8].display_name	Statistics
keywords[9].id	https://openalex.org/keywords/physics
keywords[9].score	0.16247475147247314
keywords[9].display_name	Physics
keywords[10].id	https://openalex.org/keywords/combinatorics
keywords[10].score	0.1498548984527588
keywords[10].display_name	Combinatorics
keywords[11].id	https://openalex.org/keywords/pure-mathematics
keywords[11].score	0.12373563647270203
keywords[11].display_name	Pure mathematics
language	en
locations[0].id	pmh:oai:arXiv.org:2410.20240
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2410.20240
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2410.20240
locations[1].id	doi:10.48550/arxiv.2410.20240
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2410.20240
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5073311414
authorships[0].author.orcid	https://orcid.org/0000-0003-2444-8267
authorships[0].author.display_name	B. M. Cote
authorships[0].author_position	first
authorships[0].raw_author_name	Côté, Benjamin
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5104753297
authorships[1].author.orcid	https://orcid.org/0000-0002-2111-7545
authorships[1].author.display_name	Hélène Cossette
authorships[1].author_position	middle
authorships[1].raw_author_name	Cossette, Hélène
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5055901651
authorships[2].author.orcid	https://orcid.org/0000-0001-7962-7487
authorships[2].author.display_name	Étienne Marceau
authorships[2].author_position	last
authorships[2].raw_author_name	Marceau, Etienne
authorships[2].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2410.20240
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2024-11-14T00:00:00
display_name	Centrality and shape-related comparisons in a tree-structured Markov random field
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T10064
primary_topic.field.id	https://openalex.org/fields/31
primary_topic.field.display_name	Physics and Astronomy
primary_topic.score	0.9592999815940857
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/3109
primary_topic.subfield.display_name	Statistical and Nonlinear Physics
primary_topic.display_name	Complex Network Analysis Techniques
related_works	https://openalex.org/W4229078645, https://openalex.org/W1977345676, https://openalex.org/W4282032776, https://openalex.org/W2047552823, https://openalex.org/W4321606905, https://openalex.org/W3130445735, https://openalex.org/W2105110616, https://openalex.org/W2747930654, https://openalex.org/W2739658809, https://openalex.org/W2419362237
cited_by_count	1
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	1
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2410.20240
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/2410.20240
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2410.20240
primary_location.id	pmh:oai:arXiv.org:2410.20240
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2410.20240
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2410.20240
publication_date	2024-10-26
publication_year	2024
referenced_works_count	0
abstract_inverted_index.a	14, 63, 94, 152, 167, 191, 202, 210
abstract_inverted_index.In	84
abstract_inverted_index.We	60
abstract_inverted_index.as	114
abstract_inverted_index.be	34
abstract_inverted_index.by	134, 184
abstract_inverted_index.in	36, 148
abstract_inverted_index.is	20, 40, 49, 161, 190
abstract_inverted_index.of	3, 6, 13, 27, 44, 66, 130, 143, 151, 166, 170, 177, 197
abstract_inverted_index.on	9, 127, 141, 156
abstract_inverted_index.to	56, 108, 119, 205, 209
abstract_inverted_index.we	52, 87, 124
abstract_inverted_index.Our	47
abstract_inverted_index.The	103
abstract_inverted_index.and	97, 201
abstract_inverted_index.are	106
abstract_inverted_index.but	78
abstract_inverted_index.for	22, 68, 74, 138
abstract_inverted_index.its	98
abstract_inverted_index.new	64, 115, 153
abstract_inverted_index.not	71
abstract_inverted_index.our	120
abstract_inverted_index.put	61
abstract_inverted_index.the	1, 4, 7, 10, 25, 41, 75, 80, 128, 131, 149, 164, 174, 185, 195
abstract_inverted_index.MRFs	69, 139, 172
abstract_inverted_index.This	146, 159, 188
abstract_inverted_index.also	79
abstract_inverted_index.done	162
abstract_inverted_index.into	194
abstract_inverted_index.must	33
abstract_inverted_index.only	72
abstract_inverted_index.shed	125
abstract_inverted_index.step	193
abstract_inverted_index.such	28
abstract_inverted_index.sum,	99
abstract_inverted_index.that	70
abstract_inverted_index.this	37, 39, 45, 85, 207
abstract_inverted_index.tree	8, 76, 157
abstract_inverted_index.with	173
abstract_inverted_index.work	189
abstract_inverted_index.(MRF)	19
abstract_inverted_index.MRF's	95
abstract_inverted_index.MRFs'	198
abstract_inverted_index.Tools	32
abstract_inverted_index.field	18
abstract_inverted_index.first	192
abstract_inverted_index.fixed	179
abstract_inverted_index.forth	62
abstract_inverted_index.fully	23
abstract_inverted_index.joint	11
abstract_inverted_index.light	126
abstract_inverted_index.order	155
abstract_inverted_index.serve	113
abstract_inverted_index.stone	204
abstract_inverted_index.trees	142
abstract_inverted_index.using	100
abstract_inverted_index.vein,	86
abstract_inverted_index.which	111
abstract_inverted_index.First,	51
abstract_inverted_index.Markov	16
abstract_inverted_index.choice	5
abstract_inverted_index.convex	136
abstract_inverted_index.design	150
abstract_inverted_index.family	169
abstract_inverted_index.having	178
abstract_inverted_index.pairs,	90
abstract_inverted_index.paper.	46
abstract_inverted_index.random	17, 91
abstract_inverted_index.shapes	200
abstract_inverted_index.tree's	132
abstract_inverted_index.trees'	199
abstract_inverted_index.within	163
abstract_inverted_index.Poisson	180
abstract_inverted_index.Second,	123
abstract_inverted_index.broader	211
abstract_inverted_index.compare	88
abstract_inverted_index.crucial	21
abstract_inverted_index.effects	2
abstract_inverted_index.examine	53
abstract_inverted_index.indices	117
abstract_inverted_index.models.	31
abstract_inverted_index.network	57
abstract_inverted_index.orders.	102
abstract_inverted_index.partial	154
abstract_inverted_index.regard:	38
abstract_inverted_index.results	147
abstract_inverted_index.scheme.	187
abstract_inverted_index.shapes,	133
abstract_inverted_index.shapes.	145, 158
abstract_inverted_index.theory.	59
abstract_inverted_index.vectors	92
abstract_inverted_index.accounts	73
abstract_inverted_index.analysis	160, 196, 208
abstract_inverted_index.concepts	54
abstract_inverted_index.marginal	181
abstract_inverted_index.property	176
abstract_inverted_index.specific	55
abstract_inverted_index.stepping	203
abstract_inverted_index.tailored	118
abstract_inverted_index.uncommon	175
abstract_inverted_index.component	96
abstract_inverted_index.developed	35
abstract_inverted_index.different	144
abstract_inverted_index.dynamics.	83
abstract_inverted_index.encrypted	140
abstract_inverted_index.extending	206
abstract_inverted_index.framework	165
abstract_inverted_index.graphical	30
abstract_inverted_index.influence	129
abstract_inverted_index.objective	43
abstract_inverted_index.orderings	105, 137
abstract_inverted_index.resulting	104
abstract_inverted_index.therefore	112
abstract_inverted_index.topology,	77
abstract_inverted_index.two-fold.	50
abstract_inverted_index.centrality	58, 67, 116
abstract_inverted_index.comprising	93
abstract_inverted_index.conception	65
abstract_inverted_index.dependence	186
abstract_inverted_index.discussion	48
abstract_inverted_index.exploiting	24
abstract_inverted_index.framework.	122, 212
abstract_inverted_index.stochastic	82, 101, 121
abstract_inverted_index.unaffected	183
abstract_inverted_index.underlying	81
abstract_inverted_index.overarching	42
abstract_inverted_index.quantities,	110
abstract_inverted_index.synecdochic	89
abstract_inverted_index.transferred	107
abstract_inverted_index.distribution	12
abstract_inverted_index.establishing	135
abstract_inverted_index.Understanding	0
abstract_inverted_index.distributions	182
abstract_inverted_index.probabilistic	29
abstract_inverted_index.intelligibility	26
abstract_inverted_index.risk-allocation	109
abstract_inverted_index.tree-structured	15, 171
abstract_inverted_index.propagation-based	168
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile