Related papers: Peak-Persistence Diagrams for Estimating Shapes an…

Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

In safety-critical applications like medical diagnosis, certainty associated with a model's prediction is just as important as its accuracy. Consequently, uncertainty estimation and reduction play a crucial role. Uncertainty in predictions…

The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…

In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…

In many signal processing applications, including communications, sonar, radar, and localization, a fundamental problem is the detection of a signal of interest in background noise, known as signal detection [1] [2]. A simple version of…

Shape recognition is the main challenging problem in computer vision. Different approaches and tools are used to solve this problem. Most existing approaches to object recognition are based on pixels. Pixel-based methods are dependent on…

This article introduces a new instrumental variable approach for estimating unknown population parameters with data having nonrandom missing values. With coarse and discrete instruments, Shao and Wang (2016) proposed a semiparametric method…

Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…

Gaussian Process (GP) models have also become extremely useful for optimization under uncertainty algorithms, especially where the objective functions are costly to compute. Yet, the more classical methods usually adopt strategies that, in…

Power Delay Profile (PDP) plays a crucial role in wireless communications, providing information on multipath propagation and signal strength variations over time. Accurate detection of peaks within PDP is essential to identify dominant…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e.,…

Power grid parameter estimation involves the estimation of unknown parameters, such as inertia and damping coefficients, using observed dynamics. In this work, we present a comparison of data-driven algorithms for the power grid parameter…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

We propose a precise and efficient normal estimation method that can deal with noise and nonuniform density for unstructured 3D point clouds. Unlike existing approaches that directly take patches and ignore the local neighborhood…

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…

While there has been a surge of recent interest in learning differential equation models from time series, methods in this area typically cannot cope with highly noisy data. We break this problem into two parts: (i) approximating the…