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In this paper we study supervised learning tasks on the space of probability measures. We approach this problem by embedding the space of probability measures into $L^2$ spaces using the optimal transport framework. In the embedding spaces,…

Statistics Theory · Mathematics 2022-01-27 Varun Khurana , Harish Kannan , Alexander Cloninger , Caroline Moosmüller

Amorphous materials are coming within reach of realistic computer simulations, but new approaches are needed to fully understand their intricate atomic structures. Here, we show how machine-learning (ML)-based techniques can give new,…

Hydrocarbon prospect risking is a critical application in geophysics predicting well outcomes from a variety of data including geological, geophysical, and other information modalities. Traditional routines require interpreters to go…

Machine Learning · Computer Science 2022-12-16 Ahmad Mustafa , Ghassan AlRegib

In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…

Machine Learning · Computer Science 2025-06-17 Sebastian Bordt , Eric Raidl , Ulrike von Luxburg

Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate…

Machine Learning · Computer Science 2021-10-07 Fernando Gama , Nicolas Zilberstein , Richard G. Baraniuk , Santiago Segarra

In artificial intelligence (AI), the complexity of many models and processes surpasses human understanding, making it challenging to determine why a specific prediction is made. This lack of transparency is particularly problematic in…

Machine Learning · Statistics 2025-06-30 Alexandra Stadler , Werner G. Müller , Radoslav Harman

When performing predictions that use Machine Learning (ML), we are mainly interested in performance and interpretability. This generates a natural trade-off, where complex models generally have higher skills but are harder to explain and…

Machine Learning · Computer Science 2025-03-31 Alessandro Lovo , Amaury Lancelin , Corentin Herbert , Freddy Bouchet

Recently, machine learning has emerged as an alternative, powerful approach for predicting quantum-mechanical properties of molecules and solids. Here, using kernel ridge regression and atomic fingerprints representing local environments of…

Materials Science · Physics 2018-03-08 Teppei Suzuki , Ryo Tamura , Tsuyoshi Miyazaki

Embedding molecular symmetries into machine-learning models is key for efficient learning of chemico-physical scalar properties, but little evidence on how to extend the same strategy to tensorial quantities exists. Here we formulate a…

Materials Science · Physics 2022-04-27 Vu Ha Anh Nguyen , Alessandro Lunghi

The validation of a theory is commonly based on appealing to clearly distinguishable and describable features in properly reduced experimental data, while the use of ab-initio simulation for interpreting experimental data typically requires…

Plasma Physics · Physics 2018-12-18 A. Gonoskov , E. Wallin , A. Polovinkin , I. Meyerov

Recent efforts in Machine Learning (ML) interpretability have focused on creating methods for explaining black-box ML models. However, these methods rely on the assumption that simple approximations, such as linear models or decision-trees,…

Machine Learning · Computer Science 2019-06-13 Owen Lahav , Nicholas Mastronarde , Mihaela van der Schaar

How to interpret a data mining model has received much attention recently, because people may distrust a black-box predictive model if they do not understand how the model works. Hence, it will be trustworthy if a model can provide…

Machine Learning · Computer Science 2025-03-20 Zengyou He , Pengju Li , Yifan Tang , Lianyu Hu , Mudi Jiang , Yan Liu

Obtaining microscopic structure-property relationships for grain boundaries are challenging because of the complex atomic structures that underlie their behavior. This has led to recent efforts to obtain these relationships with machine…

This paper is about a machine learning approach based on the multilinear projection of an unknown function (or probability distribution) to be estimated towards a linear (or multilinear) dimensional space E'. The proposal transforms the…

Machine Learning · Computer Science 2019-08-20 Steve Tueno

We propose a measurement framework for difficult-to-access contexts that uses indirect data traces, interpretable machine-learning models, and theory-guided triangulation to fill inaccessible measurement spaces. Many high-stakes systems of…

Machine Learning · Computer Science 2026-02-03 Margaret Foster

Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…

Statistical Mechanics · Physics 2009-11-10 Fabio D. A. Aarao Reis , Robin B. Stinchcombe

The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…

Machine Learning · Computer Science 2026-04-22 Maxim Raginsky , Benjamin Recht

The past few years have seen a rapid development of machine-learning algorithms. While surely augmenting performance, these complex tools are often treated as black-boxes and may impair our understanding of the physical processes under…

High Energy Physics - Phenomenology · Physics 2020-10-01 Gregor Kasieczka , Simone Marzani , Gregory Soyez , Giovanni Stagnitto

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

Information Theory · Computer Science 2008-06-09 Michael Chertkov , Lukas Kroc , Massimo Vergassola

There is a need of ensuring machine learning models that are interpretable. Higher interpretability of the model means easier comprehension and explanation of future predictions for end-users. Further, interpretable machine learning models…

Machine Learning · Computer Science 2020-08-17 Gregor Stiglic , Primoz Kocbek , Nino Fijacko , Marinka Zitnik , Katrien Verbert , Leona Cilar