Efficient Variational Bayes Learning of Graphical Models with Smooth Structural Changes

Efficient Variational Bayes Learning of Graphical Models with Smooth Structural Changes

Yu, Hang (NA, Ant Group CO Ltd)
Wu, Songwei (Nanyang Technological University)
Dauwels, J.H.G. (TU Delft Signal Processing Systems)

2022

Estimating a sequence of dynamic undirected graphical models, in which adjacent graphs share similar structures, is of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. Existing methods for learning dynamic graphical models require the tuning parameters that control the graph sparsity and the temporal smoothness to be selected via brute-force grid search. Furthermore, these methods are computationally burdensome with time complexity O(NP3)O(NP3) for PP variables and NN time points. As a remedy, we propose a low-complexity tuning-free Bayesian approach, named BASS. Specifically, we impose temporally dependent spike and slab priors on the graphs such that they are sparse and varying smoothly across time. An efficient variational inference algorithm based on natural gradients is then derived to learn the graph structures from the data in an automatic manner. Owing to the pseudo-likelihood and the mean-field approximation, the time complexity of BASS is only O(NP2)O(NP2). To cope with the local maxima problem of variational inference, we resort to simulated annealing and propose a method based on bootstrapping of the observations to generate the annealing noise. We provide numerical evidence that BASS outperforms existing methods on synthetic data in terms of structure estimation, while being more efficient especially when the dimension PP becomes high. We further apply the approach to the stock return data of 78 banks from 2005 to 2013 and find that the number of edges in the financial network as a function of time contains three peaks, in coincidence with the 2008 global financial crisis and the two subsequent European debt crisis. On the other hand, by identifying the frequency-domain resemblance to the time-varying graphical models, we show that BASS can be extended to learning frequency-varying inverse spectral density matrices, and further yields graphical models for multivariate stationary time series. As an illustration, we analyze scalp EEG signals of patients at the early stages of Alzheimer's disease (AD) and show that the brain networks extracted by BASS can better distinguish between the patients and the healthy controls.

Bayes methods
Brain modeling
Covariance matrices
Graphical models
inverse spectral density matrices
simulated annealing
Sparse matrices
structural changes
Time series analysis
Tuning
variational inference

http://resolver.tudelft.nl/uuid:d59b8041-2048-4cab-b5b7-33fedf316e3e

https://doi.org/10.1109/TPAMI.2022.3140886

2023-01-09

0162-8828

IEEE Transactions on Pattern Analysis and Machine Intelligence, 45 (1), 475-488

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2022 Hang Yu, Songwei Wu, J.H.G. Dauwels