相关论文: New types of nonlinear auto-correlations of bivari…

We present a method to reconstruct autocorrelated signals together with their autocorrelation structure from nonlinear, noisy measurements for arbitrary monotonous nonlinear instrument response. In the presented formulation the algorithm…

The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…

The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article we present two new…

The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is…

A transformed auto-correlation method is presented here, where a received signal is transformed based on a priori reflecting model, and then the transformed signal is cross-correlated to its original one. If the model is correct, after…

Networks where each node has one or more associated numerical values are common in applications. This work studies how summary statistics used for the analysis of spatial data can be applied to non-spatial networks for the purposes of…

A new version of the partial autocorrelation plot and a new family of subset autoregressive models are introduced. A comprehensive approach to model identification, estimation and diagnostic checking is developed for these models. These…

In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can…

The higher-order autocorrelations of integer-valued or rational-valued gridded data sets appear naturally in X-ray crystallography, and have applications in computer vision systems, correlation tomography, correlation spectroscopy, and…

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…

In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…

Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the binary sequences produced by linear shift registers with length $m$. They have a wide range of applications in communication since they have several desirable…

In this paper we introduce a new type of pattern -- a flipping correlation pattern. The flipping patterns are obtained from contrasting the correlations between items at different levels of abstraction. They represent surprising…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

The aim of this paper is to provide a new method for learning the relationships between data that have been obtained independently. Unlike existing methods like matching, the proposed technique does not require any contextual information,…

Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social…

We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for…

We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on…

Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…

The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical…