TY - JOUR
T1 - Nonparametric Fisher Geometry with Application to Density Estimation
AU - Shahbaba, Babak
AU - Lan, Shiwei
AU - Streets, Jeffrey D.
AU - Holbrook, Andrew J.
N1 - Funding Information:
This work is supported by NSF grant DMS 1622490 and NIH grant R01 MH115697.
Publisher Copyright:
© 2020 Proceedings of Machine Learning Research. All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85162669407&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85162669407&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85162669407
SN - 2640-3498
VL - 124
SP - 101
EP - 110
JO - Proceedings of Machine Learning Research
JF - Proceedings of Machine Learning Research
T2 - 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020
Y2 - 3 August 2020 through 6 August 2020
ER -