Related papers: Structured Optimal Transport
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
Domain adaptation from one data space (or domain) to another is one of the most challenging tasks of modern data analytics. If the adaptation is done correctly, models built on a specific data space become more robust when confronted to…
This article is an exposition on some recent theoretical advances in learning latent structured models, with a primary focus on the fundamental roles that optimal transport distances play in the statistical theory. We aim at what may be the…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from…
In this paper, we propose a new feature selection method for unsupervised domain adaptation based on the emerging optimal transportation theory. We build upon a recent theoretical analysis of optimal transport in domain adaptation and show…
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…
Recent studies have proposed different methods to improve multilingual word representations in contextualized settings including techniques that align between source and target embedding spaces. For contextualized embeddings, alignment…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
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…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We consider the task of building compact deep learning pipelines suitable for deployment on storage and power constrained mobile devices. We propose a unified framework to learn a broad family of structured parameter matrices that are…
Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current…
Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…