Online Estimation of Multiple Dynamic Graphs in Pattern Sequences

Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific interactions among the binary elements. To extract the dominant correlation structures and their contributions to generating data in a time-dependent manner, we model the dynamics of binary patterns using the state-space model of an Ising-type network that is composed of multiple undirected graphs. We provide a sequential Bayes algorithm to estimate the dynamics of weights on the graphs while gaining the graph structures online. This model can uncover overlapping graphs underlying the data better than a traditional orthogonal decomposition method, and outperforms an original time-dependent Ising model. We assess the performance of the method by simulated data, and demonstrate that spontaneous activity of cultured hippocampal neurons is represented by dynamics of multiple graphs.