[Submitted on 11 May 2025 (v1), last revised 22 Jul 2026 (this version, v5)]

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Abstract:Sliced optimal transport (SOT), or sliced Wasserstein (SW) distance, is widely recognized for its statistical and computational scalability. In this work, we further enhance computational scalability by proposing the first method for estimating SW from sample streams, called streaming sliced Wasserstein (Stream-SW). To define Stream-SW, we first introduce a streaming estimator of the one-dimensional Wasserstein distance (1DW). Since the 1DW has a closed-form expression, given by the integral of the absolute difference between the quantile functions of the compared distributions, we leverage quantile approximation techniques for sample streams to define a streaming 1DW estimator. By applying the streaming 1DW to all projections, we obtain Stream-SW. The key advantage of Stream-SW is its low memory complexity while providing theoretical guarantees on the approximation error. We demonstrate that Stream-SW achieves a more accurate approximation of SW than random subsampling, with lower memory consumption, when comparing Gaussian distributions and mixtures of Gaussians from streaming samples. Additionally, we conduct experiments on point cloud classification, point cloud gradient flows, and streaming change point detection to further highlight the favorable performance of the proposed Stream-SW.

Submission history

From: Khai Nguyen [view email]
[v1] Sun, 11 May 2025 04:09:24 UTC (14,491 KB)
[v2] Thu, 1 Jan 2026 05:19:06 UTC (14,491 KB)
[v3] Fri, 23 Jan 2026 22:56:37 UTC (14,492 KB)
[v4] Sun, 10 May 2026 02:10:56 UTC (14,510 KB)
[v5] Wed, 22 Jul 2026 16:17:17 UTC (14,488 KB)