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Inference of Hidden Hierarchies From Observable Networks.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Inference of Hidden Hierarchies From Observable Networks.
Author:	Pebes Trujillo, Miguel Raul.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2023
Description:	158 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: A.
Notes:	Advisor: Manrique-Vallier, Daniel;Womack, Andrew.
Contained By:	Dissertations Abstracts International85-02A.
Subject:	Statistics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30570933
ISBN:	9798379971977

Inference of Hidden Hierarchies From Observable Networks.
Pebes Trujillo, Miguel Raul.

Inference of Hidden Hierarchies From Observable Networks. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 158 p.

Source: Dissertations Abstracts International, Volume: 85-02, Section: A.

Thesis (Ph.D.)--Indiana University, 2023.

This item must not be sold to any third party vendors.

The observable dynamics of real-world networks often obey rules imposed by a hierarchical structure of their components. These hierarchies are fundamental for better understanding several natural, social, and artificial systems around us. Not surprisingly, in many phenomena these hierarchies are seldom directly observable and must be inferred only from their effects. In this dissertation, I develop a family of probabilistic models capable of inferring hidden hierarchies from observed network measurements. These models consider both the effect of hierarchies on network constituents and the structure of the hierarchies themselves. I develop estimators for latent hierarchies and computational methods to infer them under a Bayesian approach. I apply these methods to two different data structures that can be driven by an underlying hierarchy, using both simulated and real data. The first is social networks when they are used to represent affection or agonistic behavior in groups, which leads to a straightforward inference of a dominance hierarchy. The second is bipartite networks when one part can be described by a hierarchy and this hierarchy drives the co-occurrence of edges to members of the other part.I characterize hierarchies as directed acyclic graphs (DAGs). The space of hierarchies grows super-exponentially with the number of nodes in a network. This leads to both theoretical and computational inferential issues. I address both and point to avenues of research as potential extensions of my work. On the theoretical side, the main issue is to build models that are tractable while still preserving structure that is rich-enough to describe the connection of the latent hierarchy to the observable dynamics. On the computational side, it quickly becomes impossible to do an exhaustive enumeration of the space of latent hierarchies giving rise to a challenging search for the optimal solution. I deal with this by stochastically exploring the solution space via Markov Chain Monte Carlo algorithms.The developed models and methods have the potential to be widely applied in domains where revealing hidden hierarchies is meaningful. To name a few, artificial intelligence, national security, social and political sciences, international relations, animal behavior and behavioral ecology, biology, and neuroscience could benefit from these advancements. With that scope and in synergy with prior research that has characterized hierarchies differently (e.g. as total orders, rankings, dendograms, etc.), this dissertation contributes to seeding the foundations of a unified statistical framework for the study of hierarchical organization, yet to be created.

ISBN: 9798379971977Subjects--Topical Terms:

182057
Statistics.
Subjects--Index Terms:

Bayesian statistics

Inference of Hidden Hierarchies From Observable Networks.
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500 $a Source: Dissertations Abstracts International, Volume: 85-02, Section: A.
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502 $a Thesis (Ph.D.)--Indiana University, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a The observable dynamics of real-world networks often obey rules imposed by a hierarchical structure of their components. These hierarchies are fundamental for better understanding several natural, social, and artificial systems around us. Not surprisingly, in many phenomena these hierarchies are seldom directly observable and must be inferred only from their effects. In this dissertation, I develop a family of probabilistic models capable of inferring hidden hierarchies from observed network measurements. These models consider both the effect of hierarchies on network constituents and the structure of the hierarchies themselves. I develop estimators for latent hierarchies and computational methods to infer them under a Bayesian approach. I apply these methods to two different data structures that can be driven by an underlying hierarchy, using both simulated and real data. The first is social networks when they are used to represent affection or agonistic behavior in groups, which leads to a straightforward inference of a dominance hierarchy. The second is bipartite networks when one part can be described by a hierarchy and this hierarchy drives the co-occurrence of edges to members of the other part.I characterize hierarchies as directed acyclic graphs (DAGs). The space of hierarchies grows super-exponentially with the number of nodes in a network. This leads to both theoretical and computational inferential issues. I address both and point to avenues of research as potential extensions of my work. On the theoretical side, the main issue is to build models that are tractable while still preserving structure that is rich-enough to describe the connection of the latent hierarchy to the observable dynamics. On the computational side, it quickly becomes impossible to do an exhaustive enumeration of the space of latent hierarchies giving rise to a challenging search for the optimal solution. I deal with this by stochastically exploring the solution space via Markov Chain Monte Carlo algorithms.The developed models and methods have the potential to be widely applied in domains where revealing hidden hierarchies is meaningful. To name a few, artificial intelligence, national security, social and political sciences, international relations, animal behavior and behavioral ecology, biology, and neuroscience could benefit from these advancements. With that scope and in synergy with prior research that has characterized hierarchies differently (e.g. as total orders, rankings, dendograms, etc.), this dissertation contributes to seeding the foundations of a unified statistical framework for the study of hierarchical organization, yet to be created.
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653 $a Computational statistics
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