Gaussian-Dirichlet Posterior Dominance in Sequential Learning
Machine Learning
2018-02-12 v3 Machine Learning
Probability
Abstract
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.
Cite
@article{arxiv.1702.04126,
title = {Gaussian-Dirichlet Posterior Dominance in Sequential Learning},
author = {Ian Osband and Benjamin Van Roy},
journal= {arXiv preprint arXiv:1702.04126},
year = {2018}
}