Related papers: Emerging spectra of singular correlation matrices …
Time series forecasting is a fundamental tool with wide ranging applications, yet recent debates question whether complex nonlinear architectures truly outperform simple linear models. Prior claims of dominance of the linear model often…
Estimating the covariance structure of multivariate time series is a fundamental problem with a wide-range of real-world applications -- from financial modeling to fMRI analysis. Despite significant recent advances, current state-of-the-art…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the "noise". Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted…
The global sensitivity analysis of time-dependent processes requires history-aware approaches. We develop for that purpose a variance-based method that leverages the correlation structure of the problems under study and employs surrogate…
Correlated data are ubiquitous in today's data-driven society. While regression models for analyzing means and variances of responses of interest are relatively well-developed, the development of these models for analyzing the correlations…
We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the…
We study a principal component analysis problem under the spiked Wishart model in which the structure in the signal is captured by a class of union-of-subspace models. This general class includes vanilla sparse PCA as well as its variants…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
We use first-order perturbation theory to provide a local linear relation between the circuit parameters and the poles of an RLC network. The sensitivity matrix, which defines this relationship, is obtained from the systems eigenvectors and…
The inverse problem of statistical mechanics involves finding the minimal Hamiltonian that is consistent with some observed set of correlation functions. This problem has received renewed interest in the analysis of biological networks; in…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
The correlation matrix is the key element in optimal portfolio allocation and risk management. In particular, the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode, sectors and…
It was shown roughly thirty years ago that the density correlations of eigenvalues of large random matrices display a universal form, independent of most of the details of the distribution of the random matrix itself. We show that when the…
Repeated measures analyses require proper choice of the correlation model to ensure accurate inference and optimal efficiency. The linear exponent autoregressive (LEAR) correlation model provides a flexible two-parameter correlation…
We find statistically significant correlations in the cosmological matter power spectrum over the full range of observable scales. While the correlations between individual modes are weak, the band-averaged power spectrum shows strong…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…
Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…
In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral…