Title: Online Estimation of Multiple Dynamic Graphs in Pattern Sequences,
Abstract: Many time-series data including text, movies, and biological signals can be
represented as sequences of correlated binary patterns. 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 full 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.