PhD Dissertation Proposal: Andrew Zane, Causal Analysis in Mechanistic Models

Content

Speaker:

Andrew Zane

Abstract:

A statistical model represents what we observe, while a mechanistic model represents how we believe the world works. Knowing "how" lets us answer questions about cause and effect and how actions change outcomes. Domain experts have built mechanistic models iteratively over decades, often leaning on tailored theory and computational representations. At the same time, a rich toolkit for causal analysis has been developed for general-purpose graphical and statistical models, affording principled answers to causal questions under minimal assumptions. Mechanistic models, however, do not always fit this toolkit's graph-based lingua franca, and cross-disciplinary adoption has been limited.

This proposal outlines a program for bringing that causal toolkit to mechanistic models. Our work focuses on hybrid dynamical systems — a common substrate for continuous-discrete physical dynamics, and one that resists mapping onto causal graphical models. We first formalize a graph-free counterfactual semantics by defining interventions as transformations of a hybrid system's constraining equations. Unlike standard do-interventions, constraint transformations can yield ill-posedness, so we build directly on hybrid systems theory to determine when interventions preserve counterfactual measurability.

Our measurability results serve many analyses, but a large class of causal questions requires surgically manipulating specific events in a way that preserves the mechanisms connecting causes to their effects. Causal graphical models possess this alignment by construction, but generalized transformations of mechanistic models may not respect this requirement for abstract events in a simulation.

Thus, we extend causal abstraction theory to determine when a mechanistic system lifts to a unique, abstract causal model equipped with surgical interventions. A unique, consistent abstraction fully licenses all three rungs of associational, interventional, and counterfactual reasoning for admitted interventions and events — all without re-learning relationships the mechanisms already simulate, and without making general-purpose assumptions that re-purchase causal knowledge that the mechanisms already characterize.

The proposed scope of work is two-fold. First, instead of certifying identification everywhere, we propose to study tractable ways of restricting a causal analysis to the sub-world of contexts where the abstraction is identified; and second, to use those restrictions to understand when an abstraction can satisfy the identification condition yet still fail to surface a qualitatively meaningful analysis.

Advisor:

David Jensen