Statistical Methods for Percolation in Practice: Random Graph Hidden Markov Models
Abstract
Understanding the emergence of organized structure in dynamic networks remains an active research area. In the study of random networks, percolation Ðthe sudden emergence of a giant connected component (GCC)Ð is of critical importance from a theoretical, applied and statistical perspective. Interest in network percolation has been fueled by its relevance to several application domains. In clinical neuroscience, for instance, epileptic seizures have been associated with the sudden emergence of coupled activity across the brain. The resulting functional networks Ð in which edges indicate strong enough coupling between brain regions Ð are consistent with the notion of percolation. A better understanding of the type of phase transitions undergone at di?erent stages of the seizure, may aid in the development of novel strategies for the treatment of epilepsy. In turn, however, epilepsy is only one context in which seizures arise in humans Ð others being, for example, in the wake of a traumatic head injury, such as might occur in a car accident or within a military theatre of operations. The rich theory on percolation, and its application to real world data, motivates the following question: How can we distinguish between di?erent percolation regimes in practice? Previous theoretical work has concentrated on noise-free percolation, which constitutes an idealized perspective on percolation processes. In practice, however, the sampling of real-world networks is likely to be corrupted by measurement errors. Moreover, network growth has generally been conceived as a monotonic process, whereby only edge creations are allowed. However, this assumption may be too restrictive, since in real-world networks, the number of edges may increase and decrease over time, in a stochastic manner. To the best of our knowledge, there does not currently exist a statistical framework for distinguishing between di?erent types of percolation regimes in the presence of edge birth and edge death, as well as noise. We propose to develop such a framework, based on a new class of random graph hidden Markov models (RG-HMMs). This class subsumes a variety of random graph models already used in studying ideal percolation to include the additional aspects listed just above. Our work will include theoretical, methodological, and algorithmic developments for this model class that parallel those now standard for hidden Markov models in general but which, to the best of our knowledge, have yet to be extended to the context of dynamically evolving networks.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 19, 2019
- Source ID
- W911NF1810237
Entities
People
- Eric D. Kolaczyk
Organizations
- Army Contracting Command
- Boston University
- United States Army