Distributed Wasserstein Barycenteredit

A distributed Wasserstein barycenter is a probability measure that summarizes distributions held by different parties under an optimal-transport distance. Computing or approximating this shared reference requires accounting for communication and data-access constraints.¹ Xinbao Qiao studies this problem within AI and networks and data-centric ML.

Definitionedit

For local probability measures $\mu_1,\ldots,\mu_K$ with weights $\lambda_k \geq 0$ and $\sum_k \lambda_k = 1$, a $p$-Wasserstein barycenter can be written as

$$\nu^\star \in \arg\min_{\nu \in \mathcal{P}(\mathcal{X})} \sum_{k=1}^{K} \lambda_k W_p^p(\nu, \mu_k).$$

In a centralized mathematical statement, all $\mu_k$ are available to the solver. In a distributed setting, each $\mu_k$ may correspond to a local dataset, client, institution, or device. The research question therefore includes what information needs to move across the network, how much can be compressed, and whether the resulting barycenter is useful as a global distributional proxy.

Research contextedit

Distributed barycenters connect Wasserstein Geometry, Distributed Learning, and Collaborative Evaluation: a barycenter can serve as a shared reference distribution when no party has the complete data distribution. Such a reference can support model evaluation, synthetic-data verification, sample scoring, or comparison across non-identically distributed clients.

Connection to Qiao's workedit

Qiao's ICML 2026 work on sample-selection bias and model collapse already uses collaboratively computed Wasserstein-based signals to reason about synthetic-data failure under low-resource siloed access. Distributed Wasserstein barycenters continue that direction at the infrastructure level by asking how a reliable reference distribution can be computed when the evidence is split across the network, rather than assuming that evaluation data can be pooled first.

This connects to AI and networks because the computational object is shaped by the communication pattern. It connects to Synthetic Data because recursive generation needs distributional checks. It also connects to Data Centric ML because the barycenter can become a tool for deciding which data or samples matter across parties.

The under-review manuscript Decentralized Free-Support Wasserstein Barycenter develops this direction through free-support barycenter computation: learning support locations lets the shared reference adapt to distributional geometry, while separating the communication needed for barycenter quality from that needed for network agreement.

See alsoedit

• AI and Networks
• Wasserstein Geometry
• Distributed Learning
• Collaborative Evaluation
• Data Silos

Footnotesedit

1. Agueh and Carlier introduced Wasserstein-space barycenters in a SIAM paper, Barycenters in the Wasserstein Space. Cuturi and Doucet's ICML 2014 paper, Fast Computation of Wasserstein Barycenters, is a standard computational reference. ↩