UCPH Statistics Seminar: Liam Solus

Speaker: Liam Solus from KTH in Stockholm

Title: Improving structural identifiability via submodel selection

 

Abstract: When modeling causal systems with directed graphs, methods for recovering the causal graph face a natural issue: Without any additional modeling assumptions, the graph is generally unidentifiable from only observational data.  However, structural identifiability typically improves when additional constraints are learned, such as model parameter homogeneities or context-specific invariances.  One can then search a space of submodels defined by a choice of these additional constraints, returning more exact causal graphs without the need for experimental data, as we will exhibit via a pair of new causal discovery methods: one applicable to large-scale categorical data and the other to Gaussian models.  Thinking more ambitiously, we ask for methods that do not apriori impose a choice of submodel-defining constraints, but instead learn only those constraints apparent in the data. Such structure learning methods require new approaches to extracting Markov properties of submodels and proving model equivalence. We will present a general framework for investigating these problems that returns a Markov property for any model with rationally identifiable parameters.  In addition to our two examples above, this framework applies much more generally, yielding for example, a Markov property for simple directed Lyapunov models.