Streaming Sliced Wasserstein Introduced for Memory-Efficient Sample Stream Analysis

Global: Streaming Sliced Wasserstein: A New Estimator for Sample Streams

A team of machine learning researchers has unveiled a novel algorithm called Streaming Sliced Wasserstein (Stream‑SW) that estimates the sliced Wasserstein distance directly from data streams. The method promises low memory usage while delivering theoretical guarantees on approximation error, addressing a long‑standing challenge in scalable distributional comparison.

Background

Sliced optimal transport, often implemented via the sliced Wasserstein (SW) distance, is valued for its statistical robustness and computational efficiency, especially in high‑dimensional settings. Traditional SW computation, however, assumes access to the full dataset, limiting its applicability to streaming or real‑time scenarios.

Methodology

Stream‑SW builds on a streaming estimator of the one‑dimensional Wasserstein distance (1DW). Because 1DW admits a closed‑form expression as the absolute difference between quantile functions, the authors employ quantile approximation techniques that operate on continuous sample streams. By applying this streaming 1DW estimator across multiple random projections, the aggregated result constitutes the Stream‑SW metric.

Theoretical Guarantees

The authors provide formal bounds on the approximation error of Stream‑SW, demonstrating that the error diminishes as the number of projections increases and that the estimator remains unbiased under standard streaming assumptions.

Experimental Evaluation

Empirical tests compare Stream‑SW against random subsampling of data for estimating SW between Gaussian distributions and mixtures of Gaussians. Results indicate that Stream‑SW achieves higher accuracy with substantially lower memory consumption. Additional benchmarks on point‑cloud classification, point‑cloud gradient flows, and streaming change‑point detection further highlight the method’s competitive performance.

Applications

By enabling efficient, online computation of distributional distances, Stream‑SW could benefit real‑time monitoring systems, large‑scale machine‑learning pipelines, and any domain where data arrive continuously and storage is constrained.

Conclusion

The introduction of Stream‑SW represents a meaningful step toward practical, memory‑efficient optimal transport calculations on streaming data, offering both theoretical rigor and empirical effectiveness.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.