Concomitant Linear DAG Estimation
Speaker: Gonzalo Mateos
Abstract: We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of acyclicity, recent efforts have advocated a continuous constrained optimization paradigm to efficiently explore the space of DAGs. Most existing methods employ lasso-type score functions to guide this search, which (i) require expensive penalty parameter retuning when the SEM noise variances change across problem instances; and (ii) implicitly rely on limiting homoscedasticity assumptions. In this talk, I will propose a new convex score function for sparsity-aware learning of linear DAGs, which incorporates concomitant estimation of scale and thus effectively decouples the sparsity parameter from noise levels. Regularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE (Concomitant Linear DAG Estimation), a regression-based criterion amenable to efficient gradient computation and closed-form estimation of exogenous noise levels in heteroscedastic scenarios. The algorithm outperforms state-of-the-art methods without incurring added complexity, especially when the DAGs are larger, and the noise level profile is heterogeneous. CoLiDE exhibits enhanced stability manifested via reduced standard deviations in several domain-specific metrics, underscoring the robustness of the novel linear DAG estimator.
Connecting the Dots: An Updated View about How to Use Graph Signal Processing to Learn Graphs from Observations
Speaker: Antonio Marques
Abstract: Learning a graph from nodal features is a central problem in network science and statistics, with a history spanning more than 50 years. In recent years, numerous graph-learning algorithms have emerged from the field of graph signal processing (GSP). This talk has three main objectives: (i) to explain different GSP-based graph-learning methods and compare them with classical statistical approaches, (ii) to review recent GSP-based graph-learning results, and (iii) to briefly discuss current trends, challenges, and future directions. While the focus will be on the so-called network association problem (where observations from all nodes are available but no links are known), we will also consider link prediction (where some links are observed) and network tomography (where some nodes remain unobserved, relating to latent-variable graphical lasso).