Related papers: Linearized Optimal Transport pyLOT Library: A Tool…

Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…

Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…

Machine learning (ML) offers a collection of powerful approaches for detecting and modeling associations, often applied to data having a large number of features and/or complex associations. Currently, there are many tools to facilitate…

In this paper we extend recent developments in computational optimal transport to the setting of Riemannian manifolds. In particular, we show how to learn optimal transport maps from samples that relate probability distributions defined on…

Machine learning (ML) techniques have recently enabled enormous gains in sensitivity to new phenomena across the sciences. In particle physics, much of this progress has relied on excellent simulations of a wide range of physical processes.…

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…

Machine learning pipeline potentially consists of several stages of operations like data preprocessing, feature engineering and machine learning model training. Each operation has a set of hyper-parameters, which can become irrelevant for…

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…

In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…

Offline Reinforcement Learning (RL) addresses the problem of sequential decision-making by learning optimal policy through pre-collected data, without interacting with the environment. As yet, it has remained somewhat impractical, because…

Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…

Alignment is a crucial step to enhance the instruction-following and conversational abilities of language models. Despite many recent work proposing new algorithms, datasets, and training pipelines, there is a lack of comprehensive studies…

Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical…

Tree-based demappers for multiple-input multiple-output (MIMO) detection such as the sphere decoder can achieve near-optimal performance but incur high computational cost due to their sequential nature. In this paper, we propose the…

Transfer learning is an essential tool for improving the performance of primary tasks by leveraging information from auxiliary data resources. In this work, we propose Adaptive Robust Transfer Learning (ART), a flexible pipeline of…

Unsupervised action segmentation has recently pushed its limits with ASOT, an optimal transport (OT)-based method that simultaneously learns action representations and performs clustering using pseudo-labels. Unlike other OT-based…

Wasserstein distances form a family of metrics on spaces of probability measures that have recently seen many applications. However, statistical analysis in these spaces is complex due to the nonlinearity of Wasserstein spaces. One…

This paper proposes a new pipeline for long-tail (LT) recognition. Instead of re-weighting or re-sampling, we utilize the long-tailed dataset itself to generate a balanced proxy that can be optimized through cross-entropy (CE).…

This paper proposes the use of the Hellinger--Kantorovich metric from unbalanced optimal transport (UOT) in a dimensionality reduction and learning (supervised and unsupervised) pipeline. The performance of UOT is compared to that of…

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability…