Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso
This work addresses the challenge of modeling dynamic conditional dependencies in multivariate time-series for fields like finance or neuroscience, representing an incremental improvement by extending current methods to allow grouped changepoint estimation.
The authors tackled the problem of estimating time-evolving precision matrices for piecewise-constant Gaussian graphical models, proposing a novel regularized M-estimator that jointly estimates graph and changepoint structures with grouped changepoints, and demonstrated its empirical recovery in synthetic settings and application to real-world datasets.
The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data is drawn identically from a generating distribution. Introducing sparsity and sparse-difference inducing priors we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly evolving graph structures, as required. Moreover, our approach extends current methods to allow estimation of changepoints that are grouped across multiple dependencies in a system. An efficient algorithm for estimating structure is proposed. We study the empirical recovery properties in a synthetic setting. The qualitative effect of grouped changepoint estimation is then demonstrated by applying the method on two real-world data-sets.