4 papers
A Generalization of the Pearson Correlation to Riemannian Manifolds
Patrick Michl
The increasing application of deep-learning is accompanied by a shift towards highly non-linear statistical models. In terms of their geometry it is natural to identify these model…
Applications of Structural Statistics: Geometric Inference in Exponential Families
Patrick Michl
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential dist…
Foundations of Structural Statistics: Statistical Manifolds
Patrick Michl
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to…
Foundations of Structural Statistics: Topological Statistical Theory
Patrick Michl
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assu…