# Exact Dimensionality Selection for Bayesian PCA

arXiv: https://arxiv.org/abs/1703.02834 · HTML: https://mlsanity.com/paper/1703.02834/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2017.

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

- [Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles](https://mlsanity.com/paper/2507.01542/) (2025)

## Abstract (arXiv)

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal-gamma prior distribution. In this context, we exhibit a closed-form expression of the marginal likelihood which allows to infer an optimal number of components. We also propose a heuristic based on the expected shape of the marginal likelihood curve in order to choose the hyperparameters. In non-asymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state-of-the-art methods.