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. Very
recent works have attempted to incorporate a graphical perspective on some of
those model parameters, but they present notable limitations that this work
addresses. More generally, existing graphical modeling tools are designed to
incorporate either static information, focusing on statistical dependencies
among independent random variables (e.g., graphical Lasso approach), or dynamic
information, emphasizing causal relationships among time series samples (e.g.,
graphical Granger approaches). However, there are no joint approaches combining
static and dynamic graphical modeling within the context of SSMs. This work
proposes a novel approach to fill this gap by introducing a joint graphical
modeling framework that bridges the static graphical Lasso model and a
causal-based graphical approach for the linear-Gaussian SSM. We present DGLASSO
(Dynamic Graphical Lasso), a new inference method within this 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.

该研究论文提出了一种新的联合图模型框架来填补现有的状态空间模型中静态图模型和基于因果关系的图模型之间的缺失。作者通过引入一个高效的块交替主要化极小化算法实现了该框架，并通过对合成和真实气象变化数据的实验验证了所提出模型和推断算法的有效性。