Blessings of Dimensionality for Gaussian Latent Factor Models

Explore a seminar on the blessings of dimensionality for Gaussian latent factor models presented by Greg Ver Steeg from the University of Southern California. Delve into the challenges of learning graphical model structures from high-dimensional data and discover how restricting overlaps among latent factors can transform the curse of dimensionality into a blessing. Examine theoretical results suggesting that sample complexity can decrease with dimensionality under certain conditions. Learn about a novel method that leverages this blessing for high-dimensional structure recovery using limited samples. Investigate the practical applications of this approach through case studies on under-sampled data from brain fMRI and financial markets. Gain insights into topics such as mutual information, graphical models, information theory, latent remodeling, conditional independence, and unsupervised dimensionality reduction. Understand the implications for improving reproducibility in neuroscience and other fields dealing with high-dimensional data analysis.

Intro
dimensionality as an enemy
collaborators who do real problems
reducing dimensionality
making reasonable assumptions
notation
mutual information
graphical models
characterizations
models
information theory
Blessings of dimensionality
Empirical results
Latent remodeling
Normal approach
Global optimization
Conditional independence
generative model link perspective
Independence of disease
Unconstrained optimization
Cluster structure recovery
Covariance estimation
Neuroscience
Data set
Brain pictures
Factor analysis
Cluster recovery
Improving reproducibility
unsupervised dimensionality reduction
Cohens D
PCA
ICA