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Statistics Seminar - Yuexi Wang (UIUC) "Horseshoe Priors for Sparse Dirichlet-Multinomial Models"

Event Type
Department of Statistics
1306 Everitt Lab
Mar 21, 2024   3:30 pm  
Originating Calendar
Department of Statistics Event Calendar

Title: Horseshoe Priors for Sparse Dirichlet-Multinomial Models
 Abstract: Bayesian inference for Dirichlet-Multinomial (DM) models has a long and important history. The concentration parameter $\alpha$ is pivotal in smoothing category probabilities within the multinomial distribution and is crucial for the inference afterward. Due to the lack of a tractable form of its marginal likelihood, $\alpha$ is often chosen in an ad-hoc manner, or estimated using approximation algorithms. A constant $\alpha$  often leads to inadequate smoothing of probabilities, particularly for sparse compositional count datasets. In this paper, we introduce a novel class of  prior distributions facilitating conjugate updating of the concentration parameter, allowing for full Bayesian inference for DM models. Our methodology is based on fast residue computation and admits closed-form posterior moments in specific scenarios. Additionally, our prior provides continuous shrinkage with its heavy tail and  substantial mass around zero, ensuring adaptability to the sparsity or quasi-sparsity of the data. We demonstrate the usefulness of our approach on both simulated examples and on real-world applications. Finally, we conclude with directions for future research.

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