# Gaussian-Dirichlet Posterior Dominance in Sequential Learning

arXiv: https://arxiv.org/abs/1702.04126 · HTML: https://mlsanity.com/paper/1702.04126/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2017.

## Built on by (most cited first, 4 of 4)

- [From Dirichlet to Rubin: Optimistic Exploration in RL without Bonuses](https://mlsanity.com/paper/2205.07704/) (2022)
- [Deciding What to Model: Value-Equivalent Sampling for Reinforcement Learning](https://mlsanity.com/paper/2206.02072/) (2022)
- [Probabilistic Inference in Reinforcement Learning Done Right](https://mlsanity.com/paper/2311.13294/) (2023)
- [Generalized Gaussian Temporal Difference Error for Uncertainty-aware Reinforcement Learning](https://mlsanity.com/paper/2408.02295/) (2024)

## Abstract (arXiv)

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.