Derivative Causal Models: Modeling Causality at Mixed Scales of Observation

Moritz Willig, Tim Tobiasch, Jonas Seng, Devendra Singh Dhami, Kristian Kersting

Keywords: derivative causal models, causal modeling, constraint causal models

TL;DR: We propose Derivative Causal Models, a novel compact causal representation that handles mixed scales of observables in real-world systems.

Abstract:

Causal relations can materialize in many different ways. In their most simple form --typically assumed in classical causal models and discovery approaches--, similar variations of a cause lead to similar variations of an effect. However, this `smoothness' requires an observation of cause and effect just at the right scales. Unfortunately, this conflicts with records often encountered in the real-world, mixing continuous measurements with once-in-a-while observations of sparse events. Compactly modeling the causal effects between (discrete) events and continuous states is hard to achieve with classical causal models. To ease this situation, we leverage transformations that derive different scales of observables, respectively, to decompose relations and allow for compact causal representations, called Derivative Causal Models (DCM). We instantiate them using integral and derivative transforms and demonstrate that the resulting Differential Causal Models ($\partial$CM) can be discovered automatically from data.

Primary Area: causal reasoning

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Submission Number: 9470