# Prior distributions for structured semi-orthogonal matrices

arXiv: https://arxiv.org/abs/2501.10263 · HTML: https://mlsanity.com/paper/2501.10263/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [Sequential Adaptive Priors for Orthogonal Functions](https://mlsanity.com/paper/2508.15552/) (2025)

## Abstract (arXiv)

Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or smoothness. From a Bayesian perspective, these structural assumptions should be incorporated into an analysis through the prior distribution. In this work, we introduce a general approach to constructing prior distributions for structured semi-orthogonal matrices that leads to tractable posterior inference via parameter-expanded Markov chain Monte Carlo. We draw on recent results from random matrix theory to establish a theoretical basis for the proposed approach. We then introduce specific prior distributions for incorporating sparsity or smoothness and illustrate their use through applications to biological and oceanographic data.