Related papers: Gromov-Wasserstein Distance based Object Matching:…
Unsupervised object detection using deep neural networks is typically a difficult problem with few to no guarantees about the learned representation. In this work we present the first unsupervised object detection method that is…
Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between such metric measure spaces is theGromov-Wasserstein (GW)…
An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we…
Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific…
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…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…
Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…
The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW…
We develop Wasserstein-based hypothesis tests for empirical-measure convergence in stationary dependent sequences. For a known candidate invariant measure, $\mu$, we study the statistic $T_n=\sqrt{n}\,W_1(\hat\mu_n,\mu)$ and establish…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or…
In this paper we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap assisted test based on a Kolmogorov-Smirnov type statistic, which…
Background: Pose estimation of rigid objects is a practical challenge in optical metrology and computer vision. This paper presents a novel stochastic-geometrical modeling framework for object pose estimation based on observing multiple…
We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
Estimating the 6D pose for unseen objects is in great demand for many real-world applications. However, current state-of-the-art pose estimation methods can only handle objects that are previously trained. In this paper, we propose a new…