Related papers: Wasserstein metric for improved QML with adjacency…

Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising…

The problem of estimating the probability distribution of labels has been widely studied as a label distribution learning (LDL) problem, whose applications include age estimation, emotion analysis, and semantic segmentation. We propose a…

Machine learning (ML) can be used to construct surrogate models for the fast prediction of a property of interest. ML can thus be applied to chemical projects, where the usual experimentation or calculation techniques can take hours or days…

Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…

We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…

High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…

Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…

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…

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein information geometry. It defines a parametrization invariant…

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…

Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…

Seismic signals are typically compared using travel time difference or $L_2$ difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology. It exhibits properties from both of the traditional…

Designing experiments that systematically gather data from complex physical systems is central to accelerating scientific discovery. While Bayesian experimental design (BED) provides a principled, information-based framework that integrates…

Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the…

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…

With the capability to find the best fit to arbitrarily complicated data patterns, machine-learning (ML) enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states.…

In a world burdened by air pollution, the integration of state-of-the-art sensor calibration techniques utilizing Quantum Computing (QC) and Machine Learning (ML) holds promise for enhancing the accuracy and efficiency of air quality…

Within the past few years, we have witnessed the rising of quantum machine learning (QML) models which infer electronic properties of molecules and materials, rather than solving approximations to the electronic Schrodinger equation. The…