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How can we leverage domain knowledge during statistical tasks such as learning or decision-making? In this talk, we will discuss two instances of this question that arise in multi-armed bandits and causal discovery.

First, we will map contact tracing of infectious diseases to mortal multi-armed bandits where "arms" are infected people, "playing an arm" corresponds to testing a contact of that person, and "rewards" are new infections. The goal is to uncover as many infections as possible. This is a mortal bandit as each person only has a finite number of contacts. Adaptive Greedy and Pilot sampling algorithms have been previously proposed for the mortal bandits. Through Bayesian regret, we will show that both algorithms are optimal, maybe up to some logarithmic factors, in the number of arms and time horizon in big-O. Using empirical simulations, we will see that the optimal choice of algorithm depends on knowledge of the underlying infectivity (reward) distribution. We will then demonstrate these insights using three administrative COVID-19 contact tracing datasets.

Next, we will turn to causal discovery in the presence of latent confounding. Here, the directed acyclic graph (DAG) representing the underlying causal structure cannot be learned directly from observational data. Instead, by relying on conditional independence constraints present in the data, causal relationships between the observed variables may be represented by a graphical model called a maximal ancestral graph (MAG). However, several MAGs may encode the same constraints present in the observational distribution. So, we can only recover an equivalence class of MAGs, containing the true causal MAG, from observational data. We undertake the task of refining this equivalence class using expert knowledge in the form of edge orientations. To accomplish this, we revise previously established graphical orientation rules and construct new ones. We show that these rules are sound and conjecture that they are also complete for incorporating background knowledge.