# Bayesian cumulative shrinkage for infinite factorizations

arXiv: https://arxiv.org/abs/1902.04349 · HTML: https://mlsanity.com/paper/1902.04349/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2019.

## Built on by (most cited first, 12 of 12)

- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data](https://mlsanity.com/paper/2211.16403/) (2022)
- [Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data](https://mlsanity.com/paper/2310.20537/) (2023)
- [Hierarchical shrinkage Gaussian processes: applications to computer code emulation and dynamical system recovery](https://mlsanity.com/paper/2302.00755/) (2023)
- [Overfitted high-dimensional matrix factorizations via adaptive spectral shrinkage](https://mlsanity.com/paper/2606.19540/) (2026)
- [Bayesian predictive modeling of multi-source multi-way data](https://mlsanity.com/paper/2208.03396/) (2022)
- [Accelerated structured matrix factorization](https://mlsanity.com/paper/2212.06504/) (2022)
- [Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis](https://mlsanity.com/paper/2303.00473/) (2023)
- [A Bayesian Methodology for Estimation for Sparse Canonical Correlation](https://mlsanity.com/paper/2310.19621/) (2023)
- [Bayesian Tensor Decomposition with Diffusion Model Prior](https://mlsanity.com/paper/2606.03212/) (2026)
- [Shrinkage priors for Bayesian Substitute Confounders](https://mlsanity.com/paper/2606.18535/) (2026)
- [An efficient adaptive dimension selection algorithm for multidimensional probit graded response models](https://mlsanity.com/paper/2607.17654/) (2026)

## Abstract (arXiv)

There is a wide variety of models in which the dimension of the parameter space is unknown. For example, in factor analysis the number of latent factors is typically not known and has to be inferred from the observed data. Although classical shrinkage priors are useful in these contexts, increasing shrinkage priors can provide a more effective option, which progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, named the cumulative shrinkage process, for the parameters controlling the dimension in over-complete formulations. Our construction has broad applicability, simple interpretation, and is based on a sequence of spike and slab distributions which assign increasing mass to the spike as model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages over current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the methods are evaluated in simulation studies and applied to personality traits data.