The following are highlights of the work performed so far.
In the area of parameter identifiability, the team has developed new methods to decide whether the parameters of a given graphical model are identifiable (estimable) when the model features latent variables and/or feedback loops. In contrast to prior work that exploits latent independence relations the new criteria leverage latent low-rank structure.
For linear causal models, we determined novel algebraic relations among the low-order moments. These moment relations have been used to design new algorithms for causal discovery for models with non-Gaussian or homoscedastic noise. Additionally, the new results yield new insights on when different networks of cause-effect relations can be distinguished empirically in settings where not all of the relevant variables can be observed.
The existing theory and methodology for graphical models is developed primarily for recursive systems, i.e. systems that are free of feedback loops. As a novel approach that are more easily accommodates the presence of feedback loops, we are studing new classes of graphical models that are derived from dynamical processes. Our work clarifies identifiability of such models and investigates approaches to learn the models from data that lack temporal resolution.
Data-driven science often faces the difficulty that when investigating a hypothesized causal effect not only the numerical effect but also the causal model/structure has be estimated. We developed prototype methods that allow one to rigorously account for uncertainty about the direction and specific nature of cause-effect relations in statistical inference about the causal effect of one variable on another.
In causal discovery, causal directions are often determined by assessing by predicting a variable from its putative causes and assessing statistically whether the prediction errors are statistically independent of the causes. To support this approach, we worked on new approaches to formulate measures of dependence that can consistently detect non-linear dependences among random vectors, and we showed how to leverage them in formal tests of independence.
