Related papers: Measure Estimation in the Barycentric Coding Model
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in…
Given a filtration of simplicial complexes, one usually applies persistent homology and summarizes the results in barcodes. Then, in order to extract statistical information from these barcodes, one needs to compute statistical indicators…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
We study the computation of doubly regularized Wasserstein barycenters, a recently introduced family of entropic barycenters governed by inner and outer regularization strengths. Previous research has demonstrated that various…
Optimal transport maps between two probability distributions $\mu$ and $\nu$ on $\mathbb{R}^d$ have found extensive applications in both machine learning and statistics. In practice, these maps need to be estimated from data sampled…
We discuss various aspects of a local-to-global embedding technique and the metric geometry of stable metric spaces and of two of its important subclasses: locally finite spaces and proper spaces. We explain how the barycentric gluing…
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
Results concerning the construction of quantum Bayesian error regions as a means to certify the quality of parameter point estimators have been reported in recent years. This task remains numerically formidable in practice for large…
Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the…
Concept Bottleneck Model (CBM) is a methods for explaining neural networks. In CBM, concepts which correspond to reasons of outputs are inserted in the last intermediate layer as observed values. It is expected that we can interpret the…
Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a…
The Riemannian barycentre is one of the most widely used statistical descriptors for probability distributions on Riemannian manifolds. At present, existing algorithms are able to compute the Riemannian barycentre of a probability…
Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…
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…
We study the complexity of approximating Wassertein barycenter of $m$ discrete measures, or histograms of size $n$ by contrasting two alternative approaches, both using entropic regularization. The first approach is based on the Iterative…
We define a metric in the space of positive finite positive measures that extends the 2-Wasserstein metric, i.e. its restriction to the set of probability measures is the 2-Wasserstein metric. We prove a dual and a dynamic formulation and…
In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test…