Gaussian-Dirichlet Posterior Dominance in Sequential Learning
This is an incremental theoretical result for researchers analyzing sequential learning algorithms with categorical data.
The paper tackles the problem of sequential learning from categorical observations bounded in [0,1] by establishing that the Dirichlet posterior mean second-order stochastically dominates the Gaussian posterior mean under identical data with at least two observations. This provides a theoretical tool for analyzing sequential learning with categorical outcomes.
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.