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.

翻译：时序数据集在生物医学、地球观测和网络分析等众多科学与工程领域中占据核心地位。关于状态空间模型（SSMs）已有大量研究，这类强大的数学工具能够对时序数据进行概率性且可解释的学习。SSMs的模型参数估计堪称最复杂的任务之一，已知引入先验知识虽能简化解释，但会加剧推断难度。近期研究尝试将图视角融入部分模型参数，然而其存在显著局限性——这正是本文要解决的问题。更广义而言，现有图建模工具要么专注于整合静态信息（如统计独立变量间的依赖关系，例如图Lasso方法），要么聚焦于动态信息（如时间序列样本间的因果关系，例如图Granger方法），但在SSMs框架下尚缺乏融合静态与动态图建模的联合方法。本文通过引入一个桥接线性高斯SSM中静态图Lasso模型与因果图建模方法的联合图建模框架，填补了这一空白。我们提出DGLASSO（动态图Lasso）——一种在该框架内实现高效块交替最大-最小化算法的新型推断方法。通过运用非线性分析的现代工具，算法收敛性得到严格证明。在合成数据与真实气候变率数据上的实验验证，充分展示了所提模型与推断算法的有效性。