# Evaluating Sensitivity to the Stick-Breaking Prior in Bayesian Nonparametrics

arXiv: https://arxiv.org/abs/2107.03584 · HTML: https://mlsanity.com/paper/2107.03584/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 69 references that are in the map.
- First posted on arXiv 8 Jul 2021.

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

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Covariances, Robustness, and Variational Bayes](https://mlsanity.com/paper/1709.02536/) (2017)
- [Automatic Variational Inference in Stan](https://mlsanity.com/paper/1506.03431/) (2015)
- [Wasserstein Variational Inference](https://mlsanity.com/paper/1805.11284/) (2018)
- [Inconsistency of Pitman-Yor process mixtures for the number of components](https://mlsanity.com/paper/1309.0024/) (2013)
- [Sensitivity analysis for Bayesian hierarchical models](https://mlsanity.com/paper/1312.4797/) (2013)
- [Modeling with Normalized Random Measure Mixture Models](https://mlsanity.com/paper/1310.0260/) (2013)
- [Truncated Random Measures](https://mlsanity.com/paper/1603.00861/) (2016)
- [Gamma Processes, Stick-Breaking, and Variational Inference](https://mlsanity.com/paper/1410.1068/) (2014)
- [Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models](https://mlsanity.com/paper/1810.03671/) (2018)

## Built on by (most cited first, 4 of 4)

- [Black Box Variational Inference with a Deterministic Objective: Faster, More Accurate, and Even More Black Box](https://mlsanity.com/paper/2304.05527/) (2023)
- [Toward a Taxonomy of Trust for Probabilistic Machine Learning](https://mlsanity.com/paper/2112.03270/) (2021)
- [Sample Average Approximation for Black-Box VI](https://mlsanity.com/paper/2304.06803/) (2023)
- [Physics Inspired Approaches To Understanding Gaussian Processes](https://mlsanity.com/paper/2305.10748/) (2023)

## Abstract (arXiv)

Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. Prior specification is, however, relatively difficult for such models, given that their flexibility implies that the consequences of prior choices are often relatively opaque. Moreover, these choices can have a substantial effect on posterior inferences. Thus, considerations of robustness need to go hand in hand with nonparametric modeling. In the current paper, we tackle this challenge by exploiting the fact that variational Bayesian methods, in addition to having computational advantages in fitting complex nonparametric models, also yield sensitivities with respect to parametric and nonparametric aspects of Bayesian models. In particular, we demonstrate how to assess the sensitivity of conclusions to the choice of concentration parameter and stick-breaking distribution for inferences under Dirichlet process mixtures and related mixture models. We provide both theoretical and empirical support for our variational approach to Bayesian sensitivity analysis.