Sparse Graphical Linear Dynamical Systems

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

An assessment of gene regulatory network inference algorithms

A conceptual issue regarding gene regulatory network (GRN) inference algorithms is establishing their validity or correctness. In this study, we argue that for this purpose it is useful to conceive these algorithms as estimators of graph-valued parameters of explicit models for gene expression data. On this basis, we perform an assessment of a selection of influential GRN inference algorithms as estimators for two types of models: (i) causal graphs with associated structural equations models (SEMs), and (ii) differential equations models based on the thermodynamics of gene expression. Our findings corroborate that networks of marginal dependence fail in estimating GRNs, but they also suggest that the strength of statistical association as measured by mutual information may be indicative of GRN structure. Also, in simulations, we find that the GRN inference algorithms GENIE3 and TIGRESS outperform competing algorithms. However, more importantly, we also find that many observed patterns hinge on the GRN topology and the assumed data generating mechanism.Un problema conceptual con respecto a los algoritmos de inferencia de redes de regulación génica (RRG) es cómo establecer su validez. En este estudio sostenemos que para este objetivo conviene concebir estos algoritmos como estimadores de parámetros de modelos estadísticos explícitos para datos de expresión génica. Sobre esta base, realizamos una evaluación de una selección de algoritmos de inferencia de RRG como estimadores para dos tipos de modelos: (i) modelos de grafos causales asociados a modelos de ecuaciones estructurales (MEE), y (ii) modelos de ecuaciones diferenciales basados en la termodinámica de la expresion genica. Nuestros hallazgos corroboran que las redes de dependencias marginales fallan en la estimación de las RRG, pero también sugieren que la fuerza de la asociación estadística medida por la información mutua puede reflejar en cierto grado la estructura de las RRG. Además, en un estudio de simulaciones, encontramos que los algoritmos de inferencia GENIE3 y TIGRESS son los de mejor desempeño. Sin embargo, crucialmente, también encontramos que muchos patrones observados en las simulaciones dependen de la topología de la RRG y del modelo generador de datos.Maestrí