Related papers: Wasserstein Distance Regularized Sequence Represen…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

In this study, we delve into the problem of self-supervised learning (SSL) utilizing the 1-Wasserstein distance on a tree structure (a.k.a., Tree-Wasserstein distance (TWD)), where TWD is defined as the L1 distance between two tree-embedded…

Matching information across image and text modalities is a fundamental challenge for many applications that involve both vision and natural language processing. The objective is to find efficient similarity metrics to compare the similarity…

The demand of artificial intelligent adoption for condition-based maintenance strategy is astonishingly increased over the past few years. Intelligent fault diagnosis is one critical topic of maintenance solution for mechanical systems.…

Many information retrieval algorithms rely on the notion of a good distance that allows to efficiently compare objects of different nature. Recently, a new promising metric called Word Mover's Distance was proposed to measure the divergence…

Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…

The performance of unsupervised methods such as clustering depends on the choice of distance metric between features, or ground metric. Commonly, ground metrics are decided with heuristics or learned via supervised algorithms. However,…

We propose an unsupervised object matching method for relational data, which finds matchings between objects in different relational datasets without correspondence information. For example, the proposed method matches documents in…

Adversarial examples are crafted by adding indistinguishable perturbations to normal examples in order to fool a well-trained deep learning model to misclassify. In the context of computer vision, this notion of indistinguishability is…

Defining meaningful distances between samples in a dataset is a fundamental problem in machine learning. Optimal Transport (OT) lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples.…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…

To recognize objects of the unseen classes, most existing Zero-Shot Learning(ZSL) methods first learn a compatible projection function between the common semantic space and the visual space based on the data of source seen classes, then…

Knowledge transfer from a source domain to a different but semantically related target domain has long been an important topic in the context of unsupervised domain adaptation (UDA). A key challenge in this field is establishing a metric…

High-dimensional data often exhibit hierarchical structures in both modes: samples and features. Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an…

Multimodal image registration is a very challenging problem for deep learning approaches. Most current work focuses on either supervised learning that requires labelled training scans and may yield models that bias towards annotated…

The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…

Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…

We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…