相关论文: Scalable Nearest Neighbor Search for Optimal Trans…

Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…

Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…

Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable…

In this paper, we propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs). From a perspective of physical simulation, we redefine the problem of approximating the gradient flow utilizing…

We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by…

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…

Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…

Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…

This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for such an approximation (by interrupting a progressive…

Measuring the distance between ontological elements is fundamental for ontology matching. String-based distance metrics are notorious for shallow syntactic matching. In this exploratory study, we investigate Wasserstein distance targeting…

Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the…

Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate…

We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…

Many time series data mining problems can be solved with repeated use of distance measure. Examples of such tasks include similarity search, clustering, classification, anomaly detection and segmentation. For over two decades it has been…

The Fr\'echet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm…

Many data-based statistical algorithms require that one find \textit{near or nearest neighbors} to a given vector among a set of points in that vector space, usually with Euclidean topology. The k-d data structure and search algorithms are…

Emerging location-based systems and data analysis frameworks requires efficient management of spatial data for approximate and exact search. Exact similarity search can be done using space partitioning data structures, such as Kd-tree,…

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…

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

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…