Course

MATH-448: Statistical analysis of network data

Lectures in this course (26)

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Extensions to Exchangeability: Statistical Analysis of Network Data

Covers extensions to exchangeability in network data analysis, including graphon frameworks and edge exchangeability.

Biclustering: Networks MA448

Explores biclustering in data matrices, identifying coherent behavior patterns and discussing computational methods for analysis.

Network Sampling: Consistency, Models, and Dynamics

Explores network sampling consistency, models, and graph dynamics in real-life scenarios.

Latent Space Models: Inference and Applications

Explores latent space models, network representations, spectral decompositions, and parameter estimation methods.

Real-world Evidence in Health Data Sciences

Explores real-world evidence in health data sciences, highlighting observational research, reliability, and reproducibility.

Statistical Analysis of Network Data

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Exchangeability and Network Statistics

Explores exchangeability, statistical summaries for networks, invariance issues, and the Poisson Limit theorem in network statistics.

Graph Statistics: Random Graphs, Graph Homomorphisms, and Network Analysis

Explores graph statistics, random graph generation, network analysis, centrality measures, and clustering coefficients.

Stochastic Blockmodel Estimation

Explores Stochastic Blockmodel estimation, spectral clustering, network modularity, Laplacian matrix, and k-means clustering.

Block Models: Continued Analysis

Explores the stochastic blockmodel, spectral clustering, and non-parametric understanding of blockmodels, emphasizing metrics for comparing graph models.

Nonparametric Network Summaries

Covers nonparametric network summaries, centrality measures, network modularity, and clustering coefficients.

Distances and Motif Counts

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.

Network clustering

Explores network clustering, spectral clustering, k-means algorithm, eigenvalue properties, block model estimation, and structural similarity measurement.

Latent Space and RDPG: Statistical Analysis of Network Data

Covers latent space models, logistic regression, RDPG, and real-world networks.

Graph metrics: Statistical analysis

Explores graph metrics and statistical analysis in network clustering, including ERGMs application in sociology and asymptotics.

Statistical Analysis of Network Data: Noisy Sampled Networks

Explores statistical analysis of network data, covering noisy sampled networks, likelihood estimation, multilayer networks, and directed networks.

Directed Networks & Hypergraphs

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Hypergraphs and Link Prediction: Statistical Analysis of Network Data

Covers hypergraphs, complete hypergraphs, link prediction, and scoring methods in network data analysis.

Statistical Analysis of Network Data

Explores epidemics in network data, covering SIR model, basic reproductive ratio, percolation, directed networks, and maximum likelihood estimation.

Lectures in this course (26)

Statistical analysis of network data

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Extensions to Exchangeability: Statistical Analysis of Network Data

Covers extensions to exchangeability in network data analysis, including graphon frameworks and edge exchangeability.

Biclustering: Networks MA448

Explores biclustering in data matrices, identifying coherent behavior patterns and discussing computational methods for analysis.

Network Sampling: Consistency, Models, and Dynamics

Explores network sampling consistency, models, and graph dynamics in real-life scenarios.

Latent Space Models: Inference and Applications

Explores latent space models, network representations, spectral decompositions, and parameter estimation methods.

Real-world Evidence in Health Data Sciences

Explores real-world evidence in health data sciences, highlighting observational research, reliability, and reproducibility.

Statistical Analysis of Network Data

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Exchangeability and Network Statistics

Explores exchangeability, statistical summaries for networks, invariance issues, and the Poisson Limit theorem in network statistics.

Graph Statistics: Random Graphs, Graph Homomorphisms, and Network Analysis

Explores graph statistics, random graph generation, network analysis, centrality measures, and clustering coefficients.

Stochastic Blockmodel Estimation

Explores Stochastic Blockmodel estimation, spectral clustering, network modularity, Laplacian matrix, and k-means clustering.

Block Models: Continued Analysis

Explores the stochastic blockmodel, spectral clustering, and non-parametric understanding of blockmodels, emphasizing metrics for comparing graph models.

Nonparametric Network Summaries

Covers nonparametric network summaries, centrality measures, network modularity, and clustering coefficients.

Distances and Motif Counts

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.

Network clustering

Explores network clustering, spectral clustering, k-means algorithm, eigenvalue properties, block model estimation, and structural similarity measurement.

Latent Space and RDPG: Statistical Analysis of Network Data

Covers latent space models, logistic regression, RDPG, and real-world networks.

Graph metrics: Statistical analysis

Explores graph metrics and statistical analysis in network clustering, including ERGMs application in sociology and asymptotics.

Statistical Analysis of Network Data: Noisy Sampled Networks

Explores statistical analysis of network data, covering noisy sampled networks, likelihood estimation, multilayer networks, and directed networks.

Directed Networks & Hypergraphs

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Hypergraphs and Link Prediction: Statistical Analysis of Network Data

Covers hypergraphs, complete hypergraphs, link prediction, and scoring methods in network data analysis.

Statistical Analysis of Network Data

Explores epidemics in network data, covering SIR model, basic reproductive ratio, percolation, directed networks, and maximum likelihood estimation.