# Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis

arXiv: https://arxiv.org/abs/2303.00473 · HTML: https://mlsanity.com/paper/2303.00473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [Bayesian cumulative shrinkage for infinite factorizations](https://mlsanity.com/paper/1902.04349/) (2019)
- [Triple the gamma -- A unifying shrinkage prior for variance and variable selection in sparse state space and TVP models](https://mlsanity.com/paper/1912.03100/) (2019)
- [Generalized infinite factorization models](https://mlsanity.com/paper/2103.10333/) (2021)
- [Sparse Bayesian Factor Analysis when the Number of Factors is Unknown](https://mlsanity.com/paper/1804.04231/) (2018)
- [A note on the multiplicative gamma process](https://mlsanity.com/paper/1610.03408/) (2016)
- [Semiparametric Functional Factor Models with Bayesian Rank Selection](https://mlsanity.com/paper/2108.02151/) (2021)
- [Gibbs-type Indian buffet processes](https://mlsanity.com/paper/1512.02543/) (2015)
- [Sparse Bayesian time-varying covariance estimation in many dimensions](https://mlsanity.com/paper/1608.08468/) (2016)
- [Infinite Mixtures of Infinite Factor Analysers](https://mlsanity.com/paper/1701.07010/) (2017)
- [Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis](https://mlsanity.com/paper/2211.00671/) (2022)

## Abstract (arXiv)

The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (2020), which is a spike-and-slab shrinkage prior where the spike probability is stochastically increasing and constructed from the stick-breaking representation of a Dirichlet process prior. As a first contribution, this CUSP prior is extended by involving arbitrary stick-breaking representations arising from beta distributions. As a second contribution, we prove that exchangeable spike-and-slab priors, which are popular and widely used in sparse Bayesian factor analysis, can be represented as a finite generalized CUSP prior, which is easily obtained from the decreasing order statistics of the slab probabilities. Hence, exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index in the loading matrix increases, without imposing explicit order constraints on the slab probabilities. An application to sparse Bayesian factor analysis illustrates the usefulness of the findings of this paper. A new exchangeable spike-and-slab shrinkage prior based on the triple gamma prior of Cadonna et al. (2020) is introduced and shown to be helpful for estimating the unknown number of factors in a simulation study.