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Genere:Libro

Lingua: Inglese

Editore: **Chapman and Hall/CRC**

Pubblicazione: 04/2018

Edizione: 1° edizione

**Probabilistic Foundations of Statistical Network Analysis** presents a fresh and insightful perspective on the fundamental tenets and major challenges of modern network analysis. Its lucid exposition provides necessary background for understanding the essential ideas behind exchangeable and dynamic network models, network sampling, and network statistics such as sparsity and power law, all of which play a central role in contemporary data science and machine learning applications. The book rewards readers with a clear and intuitive understanding of the subtle interplay between basic principles of statistical inference, empirical properties of network data, and technical concepts from probability theory. Its mathematically rigorous, yet non-technical, exposition makes the book accessible to professional data scientists, statisticians, and computer scientists as well as practitioners and researchers in substantive fields. Newcomers and non-quantitative researchers will find its conceptual approach invaluable for developing intuition about technical ideas from statistics and probability, while experts and graduate students will find the book a handy reference for a wide range of new topics, including edge exchangeability, relative exchangeability, graphon and graphex models, and graph-valued Levy process and rewiring models for dynamic networks.

The author’s incisive commentary supplements these core concepts, challenging the reader to push beyond the current limitations of this emerging discipline. With an approachable exposition and more than 50 open research problems and exercises with solutions, this book is ideal for advanced undergraduate and graduate students interested in modern network analysis, data science, machine learning, and statistics.

**Harry Crane** is Associate Professor and Co-Director of the Graduate Program in Statistics and Biostatistics and an Associate Member of the Graduate Faculty in Philosophy at Rutgers University. Professor Crane’s research interests cover a range of mathematical and applied topics in network science, probability theory, statistical inference, and mathematical logic. In addition to his technical work on edge and relational exchangeability, relative exchangeability, and graph-valued Markov processes, Prof. Crane’s methods have been applied to domain-specific cybersecurity and counterterrorism problems at the Foreign Policy Research Institute and RAND’s Project AIR FORCE.

Dedication

Preface

Acknowledgements

- Orientation
- Binary relational data
- Network sampling
- Generative models
- Statistical modeling paradigm
- Vertex exchangeable models
- Getting beyond graphons
- Relatively exchangeable models
- Edge exchangeable models
- Relationally exchangeable models
- Dynamic network models

Analogy: Bernoulli trials

What it is: Graphs vs Networks

Moving beyond graphs

How to look at it: Labeling and representation

Where it comes from: Context

Making sense of it all: Coherence

What we’re talking about: Common examples of network data

Internet

Social networks

Karate club

Enron email corpus

Collaboration networks

Other networks

Some common scenarios

Major Open Questions

Sparsity

Modeling network complexity

Sampling issues

Modeling temporal variation

Chapter synopses and reading guide

Binary relational data

Network sampling

Generative models

Statistical modeling paradigm

Vertex exchangeable models

Getting beyond graphons

Relatively exchangeable models

Edge exchangeable models

Relationally exchangeable models

DEDICATION

Dynamic network models

Scenario: Patterns in international trade

Summarizing network structure

Dyad independence model

Exponential random graph models (ERGMs)

Scenario: Friendships in a high school

Network inference under sampling

Further reading

Opening example

Consistency under selection

Consistency in the p model

Significance of sampling consistency

Toward a coherent framework of network modeling

Selection from sparse networks

Scenario: Ego networks in high school friendships

Network sampling schemes

Relational sampling

Edge sampling

Hyperedge sampling

Path sampling

Snowball sampling

Units of observation

What is the sample size?

Consistency under subsampling

Further reading

Specification of generative models

Preferential Attachment model

Random walk models

Erd?os–R´enyi–Gilbert model

General sequential construction

Further reading

The quest for coherence

An incoherent model

What is a statistical model?

Population model

Finite sample models

Coherence

Coherence in sampling models

Coherence in generative models

Statistical implications of coherence

Examples

Erd?os–R´enyi–Gilbert model under selection sampling

ERGM with selection sampling

Erd?os–R´enyi–Gilbert model under edge sampling

Invariance principles

Further reading

Preliminaries: Formal definition of exchangeability

Implications of exchangeability

Finite exchangeable random graphs

Exchangeable ERGMs

Countable exchangeable models

Graphon models

Generative model

Exchangeability of graphon models

Aldous–Hoover theorem

Graphons and vertex exchangeability

Subsampling description

Viability of graphon models

Implication: Dense structure

Implication: Representative sampling

The emergence of graphons

Potential benefits of graphon models

Connection to de Finetti’s theorem

Graphon estimation

Further reading

Something must go

Sparse graphon models

Completely random measures and graphex models

Scenario: Formation of Facebook friendships

Network representation

Interpretation of vertex labels

Exchangeable point process models

Graphex representation

Sampling context

Further discussion

Variants of invariance

Relatively exchangeable models

DEDICATION

Edge exchangeable models

Relationally exchangeable models

Scenario: heterogeneity in social networks

Stochastic blockmodels

Generalized blockmodels

Community detection and Bayesian versions of SBM

Beyond SBMs and community detection

Relative exchangeability with respect to another network

Scenario: high school social network revisited

Exchangeability relative to a social network

Lack of interference

Label equivariance

Latent space models

Relatively exchangeable random graphs

Relatively exchangeable f-processes

Relative exchangeability under arbitrary sampling

Final remarks and further reading

Scenario: Monitoring phone calls

Edge-centric view

Edge exchangeability

Interaction propensity process

Characterizing edge exchangeable random graphs

Vertex components models

Stick-breaking constructions for vertex components

Hollywood model

The Hollywood process

Role of parameters in the Hollywood model

Statistical properties of the Hollywood model

Prediction from the Hollywood model

Thresholding

Contexts for edge sampling

Concluding remarks

Connection to graphex models

Further reading

Sampling multiway interactions (hyperedges)

Collaboration networks

Coauthorship networks

Representing multiway interaction networks

Hyperedge exchangeability

Interaction propensity process

Characterization for hyperedge exchangeable networks

Scenario: Traceroute sampling of Internet topology

Representing the data

Path exchangeability

Relational exchangeability

General Hollywood model

Markovian vertex components models

Concluding remarks and further reading

Scenario: Dynamics in social media activity

Modeling considerations

Network dynamics: Markov property

Modeling the initial state

Is the Markov property a good assumption?

Temporal Exponential Random Graph Model (TERGM)

Projectivity and sampling

Example: a TERGM for triangle counts

Projective Markov property

Rewiring chains and Markovian graphons

Exchangeable rewiring processes (Markovian graphons)

Graph-valued L´evy processes

Inference from graph-valued L´evy processes

Continuous time processes

Poissonian construction

Further reading

Bibliography

Index

ISBN: **9781138630154**

Condizione: Nuovo

Collana: Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Dimensioni: 9.25 x 6.125 in Ø 0.95 lb

Formato: Brossura

Pagine Arabe: 236

Pagine Romane: xx

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