# An optimal transportation approach for assessing almost stochastic order arXiv: https://arxiv.org/abs/1705.01788 · HTML: https://mlsanity.com/paper/1705.01788/ ## Key facts - Cited by 33 papers in the map (data through 14 Oct 2026). - First posted on arXiv 4 May 2017. ## Built on by (most cited first, 30 of 33) - [Calibrating Large Language Models Using Their Generations Only](https://mlsanity.com/paper/2403.05973/) (2024) - [Bootstrapping LLM-based Task-Oriented Dialogue Agents via Self-Talk](https://mlsanity.com/paper/2401.05033/) (2024) - [deep-significance - Easy and Meaningful Statistical Significance Testing in the Age of Neural Networks](https://mlsanity.com/paper/2204.06815/) (2022) - [Distributional Preference Alignment of LLMs via Optimal Transport](https://mlsanity.com/paper/2406.05882/) (2024) - [Exploring Predictive Uncertainty and Calibration in NLP: A Study on the Impact of Method & Data Scarcity](https://mlsanity.com/paper/2210.15452/) (2022) - [Not all layers are equally as important: Every Layer Counts BERT](https://mlsanity.com/paper/2311.02265/) (2023) - [Non-Exchangeable Conformal Language Generation with Nearest Neighbors](https://mlsanity.com/paper/2402.00707/) (2024) - [The AI Gap: How Socioeconomic Status Affects Language Technology Interactions](https://mlsanity.com/paper/2505.12158/) (2025) - [A noisy elephant in the room: Is your out-of-distribution detector robust to label noise?](https://mlsanity.com/paper/2404.01775/) (2024) - [VideoAdviser: Video Knowledge Distillation for Multimodal Transfer Learning](https://mlsanity.com/paper/2309.15494/) (2023) - [DynDepNet: Learning Time-Varying Dependency Structures from fMRI Data via Dynamic Graph Structure Learning](https://mlsanity.com/paper/2209.13513/) (2022) - [Context-aware attention layers coupled with optimal transport domain adaptation and multimodal fusion methods for recognizing dementia from spontaneous speech](https://mlsanity.com/paper/2305.16406/) (2023) - [Tokenization with Factorized Subword Encoding](https://mlsanity.com/paper/2306.07764/) (2023) - [Class Uncertainty: A Measure to Mitigate Class Imbalance](https://mlsanity.com/paper/2311.14090/) (2023) - [Generalized Attention Flow: Feature Attribution for Transformer Models via Maximum Flow](https://mlsanity.com/paper/2502.15765/) (2025) - [Putting Context in Context: the Impact of Discussion Structure on Text Classification](https://mlsanity.com/paper/2402.02975/) (2024) - [NeCA: 3D Coronary Artery Tree Reconstruction from Two 2D Projections via Neural Implicit Representation](https://mlsanity.com/paper/2409.04596/) (2024) - [BERT WEAVER: Using WEight AVERaging to enable lifelong learning for transformer-based models in biomedical semantic search engines](https://mlsanity.com/paper/2202.10101/) (2022) - [Risk Aware Benchmarking of Large Language Models](https://mlsanity.com/paper/2310.07132/) (2023) - [End-to-end Adaptive Dynamic Subsampling and Reconstruction for Cardiac MRI](https://mlsanity.com/paper/2403.10346/) (2024) - [More Room for Language: Investigating the Effect of Retrieval on Language Models](https://mlsanity.com/paper/2404.10939/) (2024) - [Multivariate Stochastic Dominance via Optimal Transport and Applications to Models Benchmarking](https://mlsanity.com/paper/2406.06425/) (2024) - [Topics as Proxies for Sociodemographics: How Conversational Context Affects LLM Answers](https://mlsanity.com/paper/2606.02776/) (2026) - [Understanding the Relation of User and News Representations in Content-Based Neural News Recommendation](https://mlsanity.com/paper/2207.14704/) (2022) - [Triggering Dark Showers with Conditional Dual Auto-Encoders](https://mlsanity.com/paper/2306.12955/) (2023) - [NeuralSolver: Learning Algorithms For Consistent and Efficient Extrapolation Across General Tasks](https://mlsanity.com/paper/2402.15393/) (2024) - [Perception-Inspired Graph Convolution for Music Understanding Tasks](https://mlsanity.com/paper/2405.09224/) (2024) - [Towards Data-Driven Electricity Management: Multi-Region Harmonized Data and Knowledge Graph](https://mlsanity.com/paper/2405.18869/) (2024) - [A multimodal LLM for the non-invasive decoding of spoken text from brain recordings](https://mlsanity.com/paper/2409.19710/) (2024) - [DuDi: Dual-Signal Distillation with Cross-Lingual Verbalizer](https://mlsanity.com/paper/2606.04694/) (2026) ## Abstract (arXiv) When stochastic dominance F≤stG does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the L2-Wasserstein distance, mathcal W2, to stochastic order of these trimmed versions. Our characterization for that distance naturally leads to consider a mathcal W2-based index of disagreement with stochastic order, varepsilonmathcal W2(F,G). We provide asymptotic results allowing to test H0: varepsilonmathcal W2(F,G)≥ varepsilon0 vs Ha: varepsilonmathcal W2(F,G)