# On the Information Processing of One-Dimensional Wasserstein Distances with Finite Samples

arXiv: https://arxiv.org/abs/2511.12881 · HTML: https://mlsanity.com/paper/2511.12881/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1903.04064/) (2019)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Wasserstein Dependency Measure for Representation Learning](https://mlsanity.com/paper/1903.11780/) (2019)
- [Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model](https://mlsanity.com/paper/1804.01947/) (2018)
- [Optimal Transport: Fast Probabilistic Approximation with Exact Solvers](https://mlsanity.com/paper/1802.05570/) (2018)
- [XceptionTime: A Novel Deep Architecture based on Depthwise Separable Convolutions for Hand Gesture Classification](https://mlsanity.com/paper/1911.03803/) (2019)
- [Kernel methods on spike train space for neuroscience: a tutorial](https://mlsanity.com/paper/1302.5964/) (2013)

## Abstract (arXiv)

Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports significantly overlap while densities exhibit substantial pointwise differences, it remains unclear whether and how this transport information can accurately identify these differences, particularly their analytic characterization in finite-sample settings. We address this issue by conducting an analysis of the information processing capabilities of the one-dimensional Wasserstein distance with finite samples. By utilizing the Poisson process and isolating the rate factor, we demonstrate the capability of capturing the pointwise density difference with Wasserstein distances and how this information harmonizes with support differences. The analyzed properties are confirmed using neural spike train decoding and amino acid contact frequency data. The results reveal that the one-dimensional Wasserstein distance highlights meaningful density differences related to both rate and support.