Learning Sparse Structural Changes in High-dimensional Markov Networks: A Review on Methodologies and Theories

For example, genes may regulate each other in different ways when external conditions are changed; the number of daily flu-like symptom reports in nearby hospitals may become correlated when a major epidemic disease breaks out; EEG signals from different regions of the brain may be synchronized/desynchronized when the subject is performing different activities. Spotting such changes in interactions may provide key insights into the underlying system. The interactions among random variables can be formulated as undirected probabilistic graphical models, or Markov Networks (MNs) [Koller and Friedman, 2009], expressing the interactions via the conditional independence. We consider a simple model: the pairwise MNs where the links are only encoded for single or pairs of random variables. Due to the Hammersley-Clifford theorem [Hammersley and Clifford, 1971], the underlying joint probability density function can be represented as the product of univariate and bivariate factors.