Related papers: CovNet: Covariance Networks for Functional Data on…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…
Graph neural networks have re-defined how we model and predict on network data but there lacks a consensus on choosing the correct underlying graph structure on which to model signals. CoVariance Neural Networks (VNN) address this issue by…
Time-dependent reliability analysis of nonlinear dynamical systems under stochastic excitations is a critical yet computationally demanding task. Conventional approaches, such as Monte Carlo simulation, necessitate repeated evaluations of…
This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…
A Covariance-on-Covariance regression model is introduced in this manuscript. It is assumed that there exists (at least) a pair of linear projections on outcome covariance matrices and predictor covariance matrices such that a log-linear…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The…
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
Heterogeneous network data with rich nodal information become increasingly prevalent across multidisciplinary research, yet accurately modeling complex nodal heterogeneity and simultaneously selecting influential nodal attributes remains an…
CoVariance Neural Networks (VNNs) perform graph convolutions on the empirical covariance matrix of signals defined over finite-dimensional Hilbert spaces, motivated by robustness and transferability properties. Yet, little is known about…
The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…
Covariance-based data processing is widespread across signal processing and machine learning applications due to its ability to model data interconnectivities and dependencies. However, harmful biases in the data may become encoded in the…
Dimension reduction is often necessary in functional data analysis, with functional principal component analysis being one of the most widely used techniques. A key challenge in applying these methods is determining the number of…
Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models…
We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…
Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…