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- W2735545481 abstract "It is well known that the Fisher information induces a Riemannian geometry on parametric families of probability density functions. We generalize this formalism to a geometry over all density functions regardless of parameterization. The resulting nonparametric Fisher information geometry is then shown to be equivalent to a familiar, albeit infinite dimensional, geometric object---the sphere. By shifting focus away from density functions and toward emph{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. This insight leads to a novel Bayesian nonparametric density estimation model. We construct the $chi^2$-process density prior by modeling the square-root density with a Gaussian process prior. Inference over square-root densities is fast, and the model retains the flexibility characteristic of Bayesian nonparametric models." @default.
- W2735545481 created "2017-07-21" @default.
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- W2735545481 date "2017-07-11" @default.
- W2735545481 modified "2023-09-27" @default.
- W2735545481 title "The nonparametric Fisher information geometry and the chi-square process density prior" @default.
- W2735545481 hasPublicationYear "2017" @default.
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