# Logistic-beta processes for dependent random probabilities with beta marginals

arXiv: https://arxiv.org/abs/2402.07048 · HTML: https://mlsanity.com/paper/2402.07048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 82 references that are in the map.
- First posted on arXiv 10 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [A multi-resolution approximation for massive spatial datasets](https://mlsanity.com/paper/1507.04789/) (2015)
- [Basis-Function Models in Spatial Statistics](https://mlsanity.com/paper/2202.03660/) (2022)
- [Poisson Random Fields for Dynamic Feature Models](https://mlsanity.com/paper/1611.07460/) (2016)
- [Dynamic Shrinkage Processes](https://mlsanity.com/paper/1707.00763/) (2017)
- [The Dependent Dirichlet Process and Related Models](https://mlsanity.com/paper/2007.06129/) (2020)
- [Bayesian dependent mixture models: A predictive comparison and survey](https://mlsanity.com/paper/2307.16298/) (2023)
- [Density regression via Dirichlet process mixtures of normal structured additive regression models](https://mlsanity.com/paper/2401.03881/) (2024)
- [Bayesian nonparametric dependent model for partially replicated data: the influence of fuel spills on species diversity](https://mlsanity.com/paper/1402.3093/) (2014)
- [Spatio-Temporal Models for Big Multinomial Data using the Conditional Multivariate Logit-Beta Distribution](https://mlsanity.com/paper/1812.03555/) (2018)
- [Stick-breaking processes with exchangeable length variables](https://mlsanity.com/paper/2008.04475/) (2020)
- [A tree perspective on stick-breaking models in covariate-dependent mixtures](https://mlsanity.com/paper/2208.02806/) (2022)
- [Structured Mixture of Continuation-ratio Logits Models for Ordinal Regression](https://mlsanity.com/paper/2211.04034/) (2022)
- [Nonparametric priors with full-range borrowing of information](https://mlsanity.com/paper/2310.00617/) (2023)

## Abstract (arXiv)

The beta distribution serves as a canonical tool for modeling probabilities in statistics and machine learning. However, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent random probabilities. We propose a novel stochastic process called the logistic-beta process, whose logistic transformation yields a stochastic process with common beta marginals. Logistic-beta processes can model dependence on both discrete and continuous domains, such as space or time, and have a flexible dependence structure through correlation kernels. Moreover, its normal variance-mean mixture representation leads to effective posterior inference algorithms. We show how the proposed logistic-beta process can be used to design computationally tractable dependent Bayesian nonparametric models, including dependent Dirichlet processes and extensions. We illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.