Time-series datasets are central in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs), which are powerful mathematical tools that allow for probabilistic and interpretable learning on time series. Estimating the model parameters in SSMs is arguably one of the most complicated tasks, and the inclusion of prior knowledge is known to both ease the interpretation but also to complicate the inferential tasks. In this talk, I will introduce a novel joint graphical modeling framework called DGLASSO (Dynamic Graphical Lasso) [1], that bridges the static graphical Lasso model [2] and the causal-based graphical approach for the linear-Gaussian SSM in [3]. I will also present a new inference method within the DGLASSO framework that implements an efficient block alternating majorization-minimization algorithm. The algorithm's convergence is established by departing from modern tools from nonlinear analysis. Experimental validation on synthetic and real weather variability data showcases the effectiveness of the proposed model and inference algorithm.
[1] E. Chouzenoux and V. Elvira. Sparse Graphical Linear Dynamical Systems. Journal of Machine Learning Research, vol. 25, no. 223, pp. 1-53, 2024
[2] J. Friedman, T. Hastie, and R. Tibshirani. Sparse inverse covariance estimation with the graphical LASSO. Biostatistics, vol. 9, no. 3, pp. 432–441, Jul. 2008.
[3] V. Elvira and E. Chouzenoux. Graphical Inference in Linear-Gaussian State-Space Models. IEEE Transactions on Signal Processing, vol. 70, pp. 4757-4771, Sep. 2022.