相关论文: Level sets estimation and Vorob'ev expectation of …

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification,…

Given a compact set $E\subset\mathbb{R}^d$ we investigate for which values of $m$ we have that $\dim_\theta P_V(E)=m$ or $\dim_\theta P_V(E)=\dim_\theta E$ for $\gamma_{d,m}-$almost all $V\in G(d,m)$. Our result can be extended to more…

We present an algorithm that takes a discrete random variable $X$ and a number $m$ and computes a random variable whose support (set of possible outcomes) is of size at most $m$ and whose Kolmogorov distance from $X$ is minimal. In addition…

The estimation of periodicity is a fundamental task in many scientific areas of study. Existing methods rely on theoretical assumptions that the observation times have equal or i.i.d. spacings, and that common estimators, such as the…

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…

Although unsupervised generative modeling of an image dataset using a Variational AutoEncoder (VAE) has been used to detect anomalous images, or anomalous regions in images, recent works have shown that this method often identifies images…

In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…

Image segmentation algorithms can be understood as a collection of pixel classifiers, for which the outcomes of nearby pixels are correlated. Classifier models can be calibrated using Inductive Conformal Prediction, but this requires…

Though neural network models demonstrate impressive performance, we do not understand exactly how these black-box models make individual predictions. This drawback has led to substantial research devoted to understand these models in areas…

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, and let $U$ be a subset of $X$ whose complement is compact. We use the exponential mixing results for diagonalizable flows on $X$ to give upper estimates for the…

This paper focuses on the analysis of conforming virtual element methods for general second-order linear elliptic problems with rough source terms and applies it to a Poisson inverse source problem with rough measurements. For the forward…

We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of…

The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…

Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate…

We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…

We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications…

This paper aims at formulating the issue of ranking multivariate unlabeled observations depending on their degree of abnormality as an unsupervised statistical learning task. In the 1-d situation, this problem is usually tackled by means of…

Random samples are extensively used to summarize massive data sets and facilitate scalable analytics. Coordinated sampling, where samples of different data sets "share" the randomization, is a powerful method which facilitates more accurate…

Population domain means are frequently expected to respect shape or order constraints that arise naturally with survey data. For example, given a job category, mean salaries in big cities might be expected to be higher than those in small…