Abstract
Artificial intelligence for causal discovery frequently uses Markov equivalence classes of directed acyclic graphs, graphically represented as essential graphs, as a way of representing uncertainty in causal directionality. There has been confusion regarding how to interpret undirected edges in essential graphs, however. In particular, experts and non-experts both have difficulty quantifying the likelihood of uncertain causal arrows being pointed in one direction or another. A simple interpretation of undirected edges treats them as having equal odds of being oriented in either direction, but I show in this paper that any agent interpreting undirected edges in this simple way can be Dutch booked. In other words, I can construct a set of bets that appears rational for the users of the simple interpretation to accept, but for which in all possible outcomes they lose money. I put forward another interpretation, prove this interpretation leads to a bet-taking strategy that is sufficient to avoid all Dutch books of this kind, and conjecture that this strategy is also necessary for avoiding such Dutch books. Finally, I demonstrate that undirected edges that are more likely to be oriented in one direction than the other are common in graphs with 4 nodes and 3 edges.
Highlights
Directed acyclic graphs (DAGs) are becoming increasingly important in fields such as epidemiology, biostatistics, operations research, and others as a tool for causal modeling and causal inference [1,2,3,4,5,6,7]
In this paper I shed some light on the interpretation of one of the most common types of output produced by causal discovery algorithms, the essential graph
When agents are trying to estimate precise quantities, such as the probability that an undirected edge in an essential graph has a particular directionality in the underlying DAG, these details become important
Summary
Artificial intelligence for causal discovery frequently uses Markov equivalence classes of directed acyclic graphs, graphically represented as essential graphs, as a way of representing uncertainty in causal directionality. There has been confusion regarding how to interpret undirected edges in essential graphs, . A simple interpretation of undirected edges treats them as having equal odds of being oriented in either direction, but I show in this paper that any agent interpreting undirected edges in this simple way can be Dutch booked. I can construct a set of bets that appears rational for the users of the simple interpretation to accept, but for which in all possible outcomes they lose money. I demonstrate that undirected edges that are more likely to be oriented in one direction than the other are common in graphs with 4 nodes and 3 edges
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