5 papers · 1 filter
Singular Fluctuation as Specific Heat in Bayesian Learning
Sean Plummer
Singular learning theory characterizes Bayesian models with non-identifiable parameterizations through two central quantities: the real log canonical threshold (RLCT), which govern…
Observable Geometry of Singular Statistical Models
Sean Plummer
Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. W…
Functional Bias and Tangent-Space Geometry in Variational Inference
Sean Plummer
Variational inference approximates Bayesian posterior distributions by projecting onto a tractable family of distributions. While most theoretical analyses evaluate the quality of…
Hypothesis Testing over Observable Regimes in Singular Models
Sean Plummer
Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the…
From Tail Universality to Bernstein-von Mises: A Unified Statistical Theory of Semi-Implicit Variational Inference
Sean Plummer
Semi-implicit variational inference (SIVI) constructs approximate posteriors of the form , where the conditional kernel is parameterized and the mixing…