相关论文: Supervised Tree-Wasserstein Distance
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
We present a novel method for efficiently searching top-k neighbors for documents represented in high dimensional space of terms based on the cosine similarity. Mostly, documents are stored as bag-of-words tf-idf representation. One of the…
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…
This paper revisits recent code similarity evaluation metrics, particularly focusing on the application of Abstract Syntax Tree (AST) editing distance in diverse programming languages. In particular, we explore the usefulness of these…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer…
We present a new space-efficient approach, (SparseDTW), to compute the Dynamic Time Warping (DTW) distance between two time series that always yields the optimal result. This is in contrast to other known approaches which typically…
Identifying document similarity has many applications, e.g., source code analysis or plagiarism detection. However, identifying similarities is not trivial and can be time complex. For instance, the Levenshtein Distance is a common metric…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct metric spaces. They are particularly useful in areas such as…
In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cost. Our algorithm is built on multilevel primal-dual…
We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared $W_2$…
The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…
The Dynamic Time Warping (DTW) distance is a popular measure of similarity for a variety of sequence data. For comparing polygonal curves $\pi, \sigma$ in $\mathbb{R}^d$, it provides a robust, outlier-insensitive alternative to the…
Dynamic time warping distance (DTW) is a widely used distance measure between time series. The best known algorithms for computing DTW run in near quadratic time, and conditional lower bounds prohibit the existence of significantly faster…