Quantum-Inspired Causal Inference

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True, correlation alone does not imply causation. But, one can extract causal conclusions from statistical data with careful assumptions. Causal inference (CI) is the nascent data science framework for doing just that. Consider: How can we determine the impact of an advertising campaign on the sales of a new product, given unmeasurable factors such as innate desirability? If we see correlation between diet and health, could that diet merely be preferred by healthier groups? How can we disentangle the impact of higher education on future wealth from factors such as aptitude or opportunity, which can also explain both educational and economic achievement? What can we learn about the roles of genes from associations between genotypes and phenotypes? These questions are unified by the theme of quantifying the cause-effect relationships between variables which are also related by hidden common causes. This is a central task in CI, and formally reduces to a low-level math problem concerning characterizing the limitations of different causal models involving hidden variables. The same low-level problem turns up in the study of the quantum physics, albeit from unrelated motivations. Physicists care about certifying the "quantumness" of their data, i.e., the failure of classical explanations in terms of (local) hidden variables. In retrospect, theoretical physicists have been doing causal inference since 1964, though the formalism of modern CI didn't emerge until some twenty years later. Significantly, the intersection of these superficially unrelated disciplines was only recognized in the last decade, by researchers at Canada's own Perimeter Institute. My research program continues Canada's first-mover advantage in the intersecting frontiers of causal inference and quantum foundations (QF). Progress in this space promises to benefit Canada's strategic priorities by improving the reliability of commercial data analysis and artificial intelligence, and in aiding the discovery of novel quantum technologies. The interdisciplinary intersection provides unique opportunities for PhD research which is both tractable and impactful. Typically, near-term research targets are either incremental or high risk. Here, however, a PhD student can practically guarantee the impact of their research. The translation of major results for QF to CI is one such avenue, as is the consideration of entirely novel questions in quantum causal inference inspired by seminal questions in the development of classical CI. Aside from being interdisciplinary, this proposal includes both basic and translational research components. Students will therefore establish a track record conducive to career paths in both industry and academia. The analytical and computational skills involved in these projects are especially portable. Students will grow into mature scientists by gaining confidence in their own problem-solving abilities and through extensive professional collaboration.