Maximum likelihood eigenfunctions of the Fokker Planck equation and Hellinger projection
نویسندگان
چکیده
We apply the L2 based Fisher-Rao vector-field projection by Brigo, Hanzon and LeGland (1999) to finite dimensional approximations of the Fokker Planck equation on exponential families. We show that if the sufficient statistics are chosen among the diffusion eigenfunctions the finite dimensional projection or the equivalent assumed density approximation provide the exact maximum likelihood density. The same result had been derived earlier by Brigo and Pistone (2016) in the infinite-dimensional Orlicz based geometry of Pistone and co-authors as opposed to the L2 structure used here. keywords Finite Dimensional Families of Probability Distributions, Exponential Families, Mixture Families, Hellinger distance, Fisher information metric, Direct L2 metric, Kullback Leibler information, Eigenfunctions, Fokker Plack equation, Forward Kolmogorov Equation, Maximum Likelihood Estimator.
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