Online Estimation of Multiple Dynamic Graphs in Pattern Sequences
This work addresses the challenge of analyzing time-series data with overlapping correlation structures for researchers in fields like neuroscience or data analysis, though it appears incremental as it builds on existing Ising models with a novel estimation approach.
The paper tackled the problem of extracting dominant correlation structures from sequences of correlated binary patterns, such as biological signals, by modeling them with a state-space Ising-type network and providing a sequential Bayes algorithm for online estimation. The result showed that the method outperformed traditional orthogonal decomposition and an original time-dependent Ising model, and it successfully represented spontaneous activity of cultured hippocampal neurons using dynamic graphs.
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.