2026-08-12 –, Room 6
Graphical models encode dependencies between variables through graphs whose implied statistical models obey algebraic constraints. We show how symbolic computation in the Julia package OSCAR enables causal effect estimation in such models. Using Groebner basis elimination, we resolve linear parameter identification beyond classical criteria and demonstrate a reproducible Julia workflow on a real data example.
Graphical models represent dependencies between variables through graphs and are widely used in causal inference and statistics. In linear structural equation models, the implied covariance relations define polynomial equations, making these models naturally accessible to methods from algebraic statistics.
In this talk, we present a Julia workflow based on the computer algebra system OSCAR to study parameter identifiability and causal effects in graphical models. Existing theory such as the half-trek criterion provides sufficient but not necessary conditions for identifiability. Using symbolic computation and Groebner basis methods, we can analyze specific models directly and determine whether parameters are generically identifiable.
Building on recent implementations in OSCAR, we demonstrate how graphical models can be translated into polynomial systems, how elimination ideals can be computed, and how resulting identification formulas can be derived automatically. This allows us to resolve cases that classical criteria leave undetermined.
The workflow is illustrated on a real data example and highlights how OSCAR.jl enables reproducible and extensible algebraic-statistical analysis for causal graphical models.
Leopold Mareis is a doctoral student in the field of applied mathematical statistics at the Technical University of Munich. He previously worked at the Fraunhofer Institute for Cognitive Systems IKS in the 'Reasoned AI Decisions' group. His research interest lies in the efficient estimation and uncertainty quantification of structural parameters in graphical modeling.