Related papers: Robust Functional Principal Component Analysis for…
Functional principal component analysis (FPCA) is a widely used technique in functional data analysis for identifying the primary sources of variation in a sample of random curves. The eigenfunctions obtained from standard FPCA typically…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
Ranked data is commonly used in research across many fields of study including medicine, biology, psychology, and economics. One common statistic used for analyzing ranked data is Kendall's {\tau} coefficient, a non-parametric measure of…
High-dimensional data models, often with low sample size, abound in many interdisciplinary studies, genomics and large biological systems being most noteworthy. The conventional assumption of multinormality or linearity of regression may…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on…
This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion:…
This paper introduces the partial Gini covariance, a novel dependence measure that addresses the challenges of high-dimensional inference with heavy-tailed errors, often encountered in fields like finance, insurance, climate, and biology.…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample…
Despite the remarkable success of deep neural networks (DNNs), the security threat of adversarial attacks poses a significant challenge to the reliability of DNNs. In this paper, both theoretically and empirically, we discover a universal…
This paper introduces an R package that implements Simultaneous non-Gaussian Component Analysis for data integration. SING uses a non-Gaussian measure of information to extract feature loadings and scores (latent variables) that are shared…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…
This article explores a general factor structure for high-dimensional nonstationary functional time series, encompassing a wide range of factor models studied in the existing literature. We investigate the asymptotic spectral behaviors of…
Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy,…
This paper establishes the functional average as an important estimand for causal inference. The significance of the estimand lies in its robustness against traditional issues of confounding. We prove that this robustness holds even when…
In this paper, we investigate and develop a new approach to the numerical analysis and characterization of random fluctuations with heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare…
Among inferential problems in functional data analysis, domain selection is one of the practical interests aiming to identify sub-interval(s) of the domain where desired functional features are displayed. Motivated by applications in…