Related papers: Gromov-Wasserstein Distance based Object Matching:…
Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…
Advancements in data collection have led to increasingly common repeated observations with complex structures in biomedical studies. Treating these observations as random objects, rather than summarizing features as vectors, avoids feature…
The aim of this paper is to present an extension of the well-known as-ymptotic equivalence between density estimation experiments and a Gaussian white noise model. Our extension consists in enlarging the nonparametric class of the…
A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete…
This paper presents a probabilistic generalization of the Generalized Optimal Sub-Pattern Assignment (GOSPA) metric, termed P-GOSPA. The GOSPA metric has been widely used to evaluate the distance between finite sets, particularly in…
We study statistical inference on the similarity/distance between two time-series under uncertain environment by considering a statistical hypothesis test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The sampling…
A fundamental challenge in data science is to match disparate point sets with each other. While optimal transport efficiently minimizes point displacements under a bijectivity constraint, it is inherently sensitive to rotations. Conversely,…
We present a framework for evaluating 6-DoF instance-level object pose estimators, focusing on those that require a single RGB (not RGB-D) image as input. Besides gaining intuition about how accurate these estimators are, we are interested…
We define a distance analogous to the Gromov-Hausdorff distance that enables the comparison of arbitrary quasi-isometric spaces. We also investigate properties preserved under limits with respect to this distance, as well as properties of…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
The paper considers a new quantitative-qualitative proximity measure for the features of information objects, where data enters a common information resource from several sources independently. The goal is to determine the possibility of…
We present a new dataset for 6-DoF pose estimation of known objects, with a focus on robotic manipulation research. We propose a set of toy grocery objects, whose physical instantiations are readily available for purchase and are…
This paper is concerned with estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its…
We consider the change-point detection in multivariate continuous and integer valued time series. We propose a Wald-type statistic based on the estimator performed by a general contrast function; which can be constructed from the…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for…
In this paper, we apply the concept of asymptotic dimension to calculating Gromov-Hausdorff distances between some unbounded metric spaces. For example, we show that the Gromov--Hausdorff between $\mathbb{R}^2$ with the Euclidean metric and…
Comparing structured data from possibly different metric-measure spaces is a fundamental task in machine learning, with applications in, e.g., graph classification. The Gromov-Wasserstein (GW) discrepancy formulates a coupling between the…