# Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixtures

arXiv: https://arxiv.org/abs/2411.14674 · HTML: https://mlsanity.com/paper/2411.14674/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Builds on (most cited first, 15 of 15)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Statistical and Topological Properties of Sliced Probability Divergences](https://mlsanity.com/paper/2003.05783/) (2020)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Distributional Sliced-Wasserstein and Applications to Generative Modeling](https://mlsanity.com/paper/2002.07367/) (2020)
- [Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds](https://mlsanity.com/paper/2403.06560/) (2024)
- [Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals](https://mlsanity.com/paper/2303.05798/) (2023)
- [Bayesian cluster analysis: Point estimation and credible balls](https://mlsanity.com/paper/1505.03339/) (2015)
- [Escaping the curse of dimensionality in Bayesian model based clustering](https://mlsanity.com/paper/2006.02700/) (2020)
- [Sharp bounds for max-sliced Wasserstein distances](https://mlsanity.com/paper/2403.00666/) (2024)
- [Search Algorithms and Loss Functions for Bayesian Clustering](https://mlsanity.com/paper/2105.04451/) (2021)
- [Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variates](https://mlsanity.com/paper/2402.01493/) (2024)
- [The Dependent Dirichlet Process and Related Models](https://mlsanity.com/paper/2007.06129/) (2020)
- [Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributions](https://mlsanity.com/paper/2404.15378/) (2024)
- [Optimal Bayesian estimators for latent variable cluster models](https://mlsanity.com/paper/1607.02325/) (2016)

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

- [Lightspeed Geometric Dataset Distance via Sliced Optimal Transport](https://mlsanity.com/paper/2501.18901/) (2025)
- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Streaming Sliced Optimal Transport](https://mlsanity.com/paper/2505.06835/) (2025)

## Abstract (arXiv)

Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al., 2022). We propose a novel approach for summarizing posterior inference in nonparametric Bayesian mixture models, prioritizing estimation of the mixing measure (or mixture) as an inference target. One of the key features is the model-agnostic nature of the approach, which remains valid under arbitrarily complex dependence structures in the underlying sampling model. Using a decision-theoretic framework, our method identifies a point estimate by minimizing posterior expected loss. A loss function is defined as a discrepancy between mixing measures. Estimating the mixing measure implies inference on the mixture density and the random partition. Exploiting the discrete nature of the mixing measure, we use a version of sliced Wasserstein distance. We introduce two specific variants for Gaussian mixtures. The first, mixed sliced Wasserstein, applies generalized geodesic projections on the product of the Euclidean space and the manifold of symmetric positive definite matrices. The second, sliced mixture Wasserstein, leverages the linearity of Gaussian mixture measures for efficient projection