Nonparametric fisher geometry with application to density estimation

Babak Shahbaba, Shiwei Lan, Jeffrey D. Streets, Andrew J. Holbrook

Research output: Contribution to conferencePaperpeer-review

Abstract

It is well known that the Fisher information induces a Riemannian geometry on parametric families of probability density functions. Following recent work, we consider the nonparametric generalization of the Fisher geometry. The resulting nonparametric Fisher geometry is shown to be equivalent to a familiar, albeit infinite-dimensional, geometric object-the sphere. By shifting focus away from density functions and toward square-root density functions, one may calculate theoretical quantities of interest with ease. More importantly, the sphere of square-root densities is much more computationally tractable. As discussed here, this insight leads to a novel Bayesian nonparametric density estimation model.

Original languageEnglish (US)
Pages101-110
Number of pages10
StatePublished - 2020
Event36th Conference on Uncertainty in Artificial Intelligence, UAI 2020 - Virtual, Online
Duration: Aug 3 2020Aug 6 2020

Conference

Conference36th Conference on Uncertainty in Artificial Intelligence, UAI 2020
CityVirtual, Online
Period8/3/208/6/20

ASJC Scopus subject areas

  • Artificial Intelligence

Fingerprint

Dive into the research topics of 'Nonparametric fisher geometry with application to density estimation'. Together they form a unique fingerprint.

Cite this