相关论文: Supervised Tree-Wasserstein Distance

In this paper, we model the document revision detection problem as a minimum cost branching problem that relies on computing document distances. Furthermore, we propose two new document distance measures, word vector-based Dynamic Time…

In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…

One approach to matching texts from asymmetrical domains is projecting the input sequences into a common semantic space as feature vectors upon which the matching function can be readily defined and learned. In real-world matching…

Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems, including transfer, multi-task, continual, and meta-learning. Most current approaches to measuring task similarities are…

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

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…

We propose a novel Wasserstein method with a distillation mechanism, yielding joint learning of word embeddings and topics. The proposed method is based on the fact that the Euclidean distance between word embeddings may be employed as the…

The Quasi Manhattan Wasserstein Distance (QMWD) is a metric designed to quantify the dissimilarity between two matrices by combining elements of the Wasserstein Distance with specific transformations. It offers improved time and space…

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…

Self-supervised learning is one of the most promising approaches to acquiring knowledge from limited labeled data. Despite the substantial advancements made in recent years, self-supervised models have posed a challenge to practitioners, as…

This paper presents a computational framework for the Wasserstein auto-encoding of merge trees (MT-WAE), a novel extension of the classical auto-encoder neural network architecture to the Wasserstein metric space of merge trees. In contrast…

The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction…

Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…

The $2$-Wasserstein distance is sensitive to minor geometric differences between distributions, making it a very powerful dissimilarity metric. However, due to this sensitivity, a small outlier mass can also cause a significant increase in…

The smooth 1-Wasserstein distance (SWD) $W_1^\sigma$ was recently proposed as a means to mitigate the curse of dimensionality in empirical approximation while preserving the Wasserstein structure. Indeed, SWD exhibits parametric convergence…

Word Mover's Distance (WMD) computes the distance between words and models text similarity with the moving cost between words in two text sequences. Yet, it does not offer good performance in sentence similarity evaluation since it does not…

The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…

We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high…