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Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…
Causal disentanglement seeks a representation of data involving latent variables that relate to one another via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed…
Singular value decomposition is the key tool in the analysis and understanding of linear regularization methods. In the last decade nonlinear variational approaches such as $\ell^1$ or total variation regularizations became quite prominent…
We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and…
We propose a framework combining detrended fluctuation analysis with standard regression methodology. The method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and…
We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our $\beta$-TCVAE (Total Correlation Variational Autoencoder), a refinement of the…
This paper is motivated by modeling the cycle-to-cycle variability associated with the resistive switching operation behind memristors. As the data are by nature curves, functional principal component analysis is a suitable candidate to…
Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there…
The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue…
Principal loading analysis is a dimension reduction method that discards variables which have only a small distorting effect on the covariance matrix. As a special case, principal loading analysis discards variables that are not correlated…
We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability…
It was found that the vector meson pair from the pseudoscalar decays can form an entangled state. In this work we give out detailed explanations on the polarization correlation of the two entangled vector mesons. It is demonstrated that an…
Vector couplings in the Duffin-Kemmer-Petiau theory are revised. It is shown that minimal and nonminimal vector potentials behave differently under charge-conjugation and time-reversal transformations. In particular, it is shown that…
In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…
Latent traversal is a popular approach to visualize the disentangled latent representations. Given a bunch of variations in a single unit of the latent representation, it is expected that there is a change in a single factor of variation of…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
Motivated by the simultaneous association analysis with the presence of latent confounders, this paper studies the large-scale hypothesis testing problem for the high-dimensional confounded linear models with both non-asymptotic and…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate…