Categories for AI talk: Causal Model Abstraction & Grounding via Category Theory - by Taco Cohen

Motivated by the recent emergence of category theory in machine learning, we teach a course on its philosophy, applications and outlook from the perspective of machine learning!

See for more information: https://cats.for.ai/

In this second invited talk, Taco will survey the literature on category theory and causality and discuss his paper "Towards a Grounded Theory of Causation for Embodied AI" (https://arxiv.org/abs/2206.13973)

Abstract:
Causal models are used in many areas of science to describe data generating processes and reason about the effect of changes to these processes (interventions). Causal models are typically highly abstracted representations of the underlying process, consisting of only a few carefully selected variables, and the causal mechanisms between them. This simplifies causal reasoning, but the relation between the model and the underlying system is never described in mathematical terms, and this has led to considerable philosophical confusions. Furthermore, it has made it hard to understand how causal modeling relates to other fields such as physics (where systems are described by dynamical laws without reference to causes), dynamical systems, and agent-centric frameworks such as Markov Decision Processes (MDPs). In this talk we study this idea of abstraction from a categorical perspective, focussing on two questions in particular:
1. What is an appropriate notion of morphism between causal models? When can we say that one model is an abstraction of another? How can we set up a convenient category of causal models?
2. What does it mean for a causal model to be an abstraction of an underlying dynamical system or Markov decision process?
To answer the first question we will mainly survey the existing literature, while for the second we will present a new approach to grounding causal models in dynamical systems and MDPs via natural transformations, and giving for the first time a mathematical definition of "causal mechanism" as a functional relationship between outcome variables that is invariant to interventions (modelled as transformations of the state space).