We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network M on a graph with n discrete variables and bounded in-degree and bounded confounded components'', we show that O(log n) interventions on an unknown causal Bayesian network X on the same graph, and O(n/epsilon 2) samples per intervention, suffice to efficiently distinguish whether X M or whether there exists some intervention under which X and M are farther than epsilon in total variation distance. We also obtain sample/time/intervention efficient algorithms for: (i) testing the identity of two unknown causal Bayesian networks on the same graph; and (ii) learning a causal Bayesian network on a given graph. Although our algorithms are non-adaptive, we show that adaptivity does not help in general: Omega(log n) interventions are necessary for testing the identity of two unknown causal Bayesian networks on the same graph, even adaptively. Our algorithms are enabled by a new subadditivity inequality for the squared Hellinger distance between two causal Bayesian networks.
Reinforcement Learning (RL) is a heuristic method for learning locally optimal policies in Markov Decision Processes (MDP). Its classical formulation (Sutton & Barto 1998) maintains point estimates of the expected values of states or state-action pairs. Bayesian RL (Dearden, Friedman, & Russell 1998) extends this to beliefs over values. However the concept of values sits uneasily with the original notion of Bayesian Networks (BNs), which were defined (Pearl 1988) as having explicitly causal semantics. In this paper we show how Bayesian RL can be cast in an explicitly Bayesian Network formalism, making use of backwards-in-time causality. We show how the heuristic used by RL can be seen as an instance of a more general BN inference heuristic, which cuts causal links in the network and replaces them with noncausal approximate hashing links for speed. This view brings RL into line with standard Bayesian AI concepts, and suggests similar hashing heuristics for other general inference tasks.
This paper describes a Bayesian method for combining an arbitrary mixture of observational and experimental data in order to learn causal Bayesian networks. Observational data are passively observed. Experimental data, such as that produced by randomized controlled trials, result from the experimenter manipulating one or more variables (typically randomly) and observing the states of other variables. The paper presents a Bayesian method for learning the causal structure and parameters of the underlying causal process that is generating the data, given that (1) the data contains a mixture of observational and experimental case records, and (2) the causal process is modeled as a causal Bayesian network. This learning method was applied using as input various mixtures of experimental and observational data that were generated from the ALARM causal Bayesian network. In these experiments, the absolute and relative quantities of experimental and observational data were varied systematically. For each of these training datasets, the learning method was applied to predict the causal structure and to estimate the causal parameters that exist among randomly selected pairs of nodes in ALARM that are not confounded. The paper reports how these structure predictions and parameter estimates compare with the true causal structures and parameters as given by the ALARM network.
We provide a conceptual map to navigate causal analysis problems. Focusing on the case of discrete random variables, we consider the case of causal effect estimation from observational data. The presented approaches apply also to continuous variables, but the issue of estimation becomes more complex. We then introduce the four schools of thought for causal analysis
We offer a complete characterization of the set of distributions that could be induced by local interventions on variables governed by a causal Bayesian network. We show that such distributions must adhere to three norms of coherence, and we demonstrate the use of these norms as inferential tools in tasks of learning and identification. Testable coherence norms are subsequently derived for networks containing unmeasured variables.