# Vertical Consensus Inference for High-Dimensional Random Partition

arXiv: https://arxiv.org/abs/2603.27864 · HTML: https://mlsanity.com/paper/2603.27864/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 63 references that are in the map.
- First posted on arXiv 29 Mar 2026.

## Builds on (most cited first, 22 of 22)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [Scalable Bayes via Barycenter in Wasserstein Space](https://mlsanity.com/paper/1508.05880/) (2015)
- [Asymptotically Exact, Embarrassingly Parallel MCMC](https://mlsanity.com/paper/1311.4780/) (2013)
- [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)
- [Parallelizing MCMC via Weierstrass Sampler](https://mlsanity.com/paper/1312.4605/) (2013)
- [Are Gibbs-type priors the most natural generalization of the Dirichlet process?](https://mlsanity.com/paper/1503.00163/) (2015)
- [Search Algorithms and Loss Functions for Bayesian Clustering](https://mlsanity.com/paper/2105.04451/) (2021)
- [Variational consensus Monte Carlo](https://mlsanity.com/paper/1506.03074/) (2015)
- [Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation](https://mlsanity.com/paper/2404.09113/) (2024)
- [Likelihood Inflating Sampling Algorithm](https://mlsanity.com/paper/1605.02113/) (2016)
- [Centered Partition Process: Informative Priors for Clustering](https://mlsanity.com/paper/1901.10225/) (2019)
- [Consensus Monte Carlo for Random Subsets using Shared Anchors](https://mlsanity.com/paper/1906.12309/) (2019)
- [Interpolating between Optimal Transport and KL regularized Optimal Transport using R'enyi Divergences](https://mlsanity.com/paper/2404.18834/) (2024)
- [Using the left Gram matrix to cluster high dimensional data](https://mlsanity.com/paper/2202.08236/) (2022)
- [A Fast Algorithm for Clustering High Dimensional Feature Vectors](https://mlsanity.com/paper/1811.00956/) (2018)

## Built on by (most cited first, 1 of 1)

- [Sliced-Regularized Optimal Transport](https://mlsanity.com/paper/2604.23944/) (2026)

## Abstract (arXiv)

We review recently proposed Bayesian approaches for clustering high-dimensional data. After identifying the main limitations of available approaches, we introduce an alternative framework based on vertical consensus inference (VCI) to mitigate the curse of dimensionality in high-dimensional Bayesian clustering. VCI builds on the idea of consensus Monte Carlo by dividing the data into multiple shards (smaller subsets of variables), performing posterior inference on each shard, and then combining the shard-level posteriors to obtain a consensus posterior. The key distinction is that VCI splits the data vertically, producing vertical shards that retain the same number of observations but have lower dimensionality. We use an entropic regularized Wasserstein barycenter to define a consensus posterior. The shard-specific barycenter weights are constructed to favor shards that provide meaningful partitions, distinct from a trivial single cluster or all singleton clusters, favoring balanced cluster sizes and precise shard-specific posterior random partitions. We show that VCI can be interpreted as a variational approximation to the posterior under a hierarchical model with a generalized Bayes prior. For relatively low-dimensional problems, experiments suggest that VCI closely approximates inference based on clustering the entire multivariate data. For high-dimensional data and in the presence of many noninformative dimensions, VCI introduces a new framework for model-based and principled inference on random partitions. Although our focus here is on random partitions, VCI can be applied to any dimension-independent parameters and serves as a bridge to emerging areas in statistics such as consensus Monte Carlo, optimal transport, variational inference, and generalized Bayes.