Whitening as a tool for estimating mutual information in spatiotemporal data sets
For a pair of time series \(x_t\) and \(y_t\), \(t=1, \dots , N_t\), the authors define the mutual information between \(x\) and \(y\) by \[ I(x,y)=\log p((x_1,y_1),\dots , (x_{N_t},y_{N_t})) - \log(p(x_1,\dots , x_{N_t})p(y_1,\dots , y_{N_t})), \] where \(p\) denotes the corresponding joint distribution, and in the joint distribution of all elements of both time series the elements are ordered as pairs. The aim of the paper is to clarify the relations between predictive modelling, maximum likelihood estimation, model comparison, linear correlation and mutual information. The authors interpret modelling as a process of spatial and temporal whitening of the raw data, i.e., transforming it into spatially and temporally uncorrelated innovations. A parsimonious multivariate autoregressive model based on nearest-neighbour interactions is employed. The paper concentrates on the presentation of the methodology and its theoretical background, assuming just the presence of a spatially extended dynamical system, from which the spatiotemporal data has been recorded. Nevertheless, the authors illustrate the practical applications of the methodology by showing results of analysing simulated data sets generated by a system of coupled stochastic oscillators.
scientific article; zbMATH DE number 5080740
scientific article