A Probabilistic Calculus of Actions
This work addresses the challenge of reasoning about actions and policies in domains with mixed probabilistic and causal information, which is incremental as it builds on existing causal and probabilistic frameworks.
The paper tackles the problem of quantifying the effects of actions and observations from partially specified probabilistic and causal knowledge by introducing a symbolic calculus that integrates both types of conditioning. It enables derivation of new conditional probabilities, including causal effects, from incomplete data like Bayesian networks.
We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of conditioning operators: ordinary Bayes conditioning, P(y|X = x), which represents the observation X = x, and causal conditioning, P(y|do(X = x)), read the probability of Y = y conditioned on holding X constant (at x) by deliberate action. Given a mixture of such observational and causal sentences, together with the topology of the causal graph, the calculus derives new conditional probabilities of both types, thus enabling one to quantify the effects of actions (and policies) from partially specified knowledge bases, such as Bayesian networks in which some conditional probabilities may not be available.