A Probabilistic Calculus of Actions

TL;DR

This paper introduces a symbolic calculus that combines probabilistic and causal reasoning, allowing for the derivation of probabilistic effects of actions and observations within complex domains.

Contribution

It presents a novel calculus integrating Bayesian and causal conditioning, enabling probabilistic inference from partially specified causal models.

Findings

Derives new conditional probabilities from mixed observational and causal data.

Handles incomplete Bayesian networks with missing conditional probabilities.

Quantifies effects of actions and policies in uncertain domains.

Abstract

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.