Dissertation
Dynamic causality: sparse symbolic regression as a tool to learn causal dynamic structural equations with applications to counterfactuals
Doctor of Philosophy (Ph.D.), Drexel University
Mar 2024
DOI:
https://doi.org/10.17918/00001922
Abstract
Learning governing equations of dynamic systems from data is an important open problem in machine learning and system identification. One of the most successful algorithms to date, SINDy, uses sparse regression to learn the governing equations of dynamical system from data. Despite its success across many domains, it makes the implausible assumptions that researchers will always know exactly which variables are part of the system in question and which functions would be a good basis to express the governing equations in. In this work, I explore how the SINDy algorithm can be augmented to work even in the more realistic scenario where these assumptions don't hold. With respect to the assumption of prior system variable knowledge, I show how solving this problem reduces to solving the problem of causal discovery, and how state-of-the art causal discovery algorithms can be used to eliminate the need for this assumption. To solve the problem of needing to know a set of basis functions a priori, I adapted the sparse coding algorithm to learn a functional basis from data. These results are then combined to show how SINDy can be augmented to work when neither the exact number of variables in the system nor a functional basis is known a priori. The final portion of my research shows how my work can be applied to the field of algorithmic recourse in explainable artificial intelligence. In my research, I show how causally robust governing equations can be used to generate algorithmic recourse recommendations that, if acted upon, will not cause the underlying distribution to shift. These are known as meaningful recourse recommendations. I also show how existing counterfactual generation methods fail in the multi-agent case and suggest how causally augmented SINDy could be used to solve this problem.
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Details
- Title
- Dynamic causality
- Creators
- Andrew O'Brien
- Contributors
- Edward Kim (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- xv, 92 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- Computer Science (Computing) (2013-2026); College of Computing and Informatics (2013-2026); Drexel University
- Other Identifier
- 991021853710904721