Title: Bounding Counterfactuals in Hidden Markov Models (joint work with Martin Haugh)

Abstract. Answering a counterfactual query in a hidden Markov model (HMM) requires embedding the HMM in a structural causal model. In general, however, we do not have sufficient information to fully specify the structural causal model and so we cannot provide an exact answer to the counterfactual query. Knowing the structure of the HMM, however, allows us to dramatically simply the space of feasible structural causal models and we optimize over this space to compute upper and lower bounds on the counterfactual query. Our work brings together ideas from causality, state-space models, simulation, and optimization (sample average approximation and polynomial programs), and to the best of our knowledge, we are the first to bound counterfactual queries in a HMM. Our optimization-based framework allows us to encode domain-specific knowledge as constraints over the structural causal model, resulting in tighter bounds. We use this technique to disprove a recent conjecture suggesting that the Gumbel-max distribution is the unique mechanism for modeling structural causal models with the "counterfactual stability" property. In addition, we show how informative bounds can still be computed even when the original polynomial programs are too difficult to solve. Finally, we demonstrate the application of our framework on a data-driven breast cancer case study, where we bound the "probability of necessity". In particular, we consider a patient who died from breast cancer after being denied regular screenings by her insurance company, and we bound the probability she would not have died had the screenings been permitted.

Full paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4529724

Preliminary version appeared in ICML: https://proceedings.mlr.press/v202/haugh23a/haugh23a.pdf

Bio. Raghav Singal is an Assistant Professor (Wei-Chung Bradford Hu T'89 Faculty Fellow) in the Operations and Management Science group at the Tuck School of Business (Dartmouth College). His research focuses on analytics in a mix of marketplaces. He leverages data to develop application-driven models that help businesses evaluate complex systems and make better decisions. More information can be found here: https://www.columbia.edu/~rs3566/