# Sparse Graphical Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2307.03210 · HTML: https://mlsanity.com/paper/2307.03210/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 85 references that are in the map.
- First posted on arXiv 6 Jul 2023.

## Builds on (most cited first, 19 of 19)

- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data](https://mlsanity.com/paper/1511.02746/) (2015)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2010.12133/) (2020)
- [Learning to Discover Sparse Graphical Models](https://mlsanity.com/paper/1605.06359/) (2016)
- [A Proximal Approach for a Class of Matrix Optimization Problems](https://mlsanity.com/paper/1801.07452/) (2018)
- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [Semi-Blind Inference of Topologies and Dynamical Processes over Graphs](https://mlsanity.com/paper/1805.06095/) (2018)
- [Graph Kalman Filters](https://mlsanity.com/paper/2303.12021/) (2023)
- [Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering](https://mlsanity.com/paper/1711.09306/) (2017)
- [Sparse Bayesian Estimation of Parameters in Linear-Gaussian State-Space Models](https://mlsanity.com/paper/2306.11652/) (2023)
- [Iterated Extended Kalman Smoother-based Variable Splitting for L1-Regularized State Estimation](https://mlsanity.com/paper/1903.08605/) (2019)
- [GraphEM: EM algorithm for blind Kalman filtering under graphical sparsity constraints](https://mlsanity.com/paper/2001.03195/) (2020)
- [SPOQ ℓp-Over-ℓq Regularization for Sparse Signal Recovery applied to Mass Spectrometry](https://mlsanity.com/paper/2001.08496/) (2020)
- [GraphIT: Iterative reweighted ℓ1 algorithm for sparse graph inference in state-space models](https://mlsanity.com/paper/2303.12569/) (2023)

## Built on by (most cited first, 4 of 4)

- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Spatiotemporal graph neural process for reconstruction, extrapolation, and classification of cardiac trajectories](https://mlsanity.com/paper/2509.12953/) (2025)
- [Truncated Neural Likelihood Estimation for Simulation-Based Inference in State-Space Models](https://mlsanity.com/paper/2605.21805/) (2026)
- [FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference](https://mlsanity.com/paper/2609.29216/) (2026)

## Abstract (arXiv)

Time-series datasets are central in machine learning with applications 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. Learning 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 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 various synthetic data showcases the effectiveness of the proposed model and inference algorithm.