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2017

Gaussian-Dirichlet Posterior Dominance in Sequential Learning

Osband, Ian, Van Roy, Benjamin

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We consider the problem of sequential learning from categorical observations bounded in [0,1].

We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise.
We establish that, conditioned upon identical data with at least two observations, the posterior mean of the categorical distribution will always second-order stochastically dominate the posterior mean of the Gaussian distribution.
These results provide a useful tool for the analysis of sequential learning under categorical outcomes.

Gaussian-Dirichlet Posterior Dominance in Sequential Learning · Around

Built on

Principles of mathematical analysis , volume 3
Walter Rudin · 1964
Earlier work this paper cites.
Rules for ordering uncertain prospects
Josef Hadar and William R Russell · 1969
Earlier work this paper cites.
Mixtures of dirichlet processes with applications to bayesian nonparametric problems
Charles E Antoniak · 1974
Earlier work this paper cites.

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