Related papers: Constructing Exact Confidence Regions on Parameter…

Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine…

Functional data analysis, FDA, is now a well established discipline of statistics, with its core concepts and perspectives in place. Despite this, there are still fundamental statistical questions which have received relatively little…

A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…

To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic. We also study confidence regions based on the likelihood…

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the…

In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually…

We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…

This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…

In this paper, we present a novel unpaired point cloud completion network, named Cycle4Completion, to infer the complete geometries from a partial 3D object. Previous unpaired completion methods merely focus on the learning of geometric…

Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…

The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…

The asymptotic results pertaining to the distribution of the log likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two and three dimensional regions can be displayed…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a high-order immersed boundary technique that computes on a…

We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…

Introduction: Computational modeling has rapidly advanced over the last decades, especially to predict molecular properties for chemistry, material science and drug design. Recently, machine learning techniques have emerged as a powerful…

Confidence nets, that is, collections of confidence intervals that fill out the parameter space and whose exact parameter coverage can be computed, are familiar in nonparametric statistics. Here, the distributional assumptions are based on…

We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly…