Identifiability in Causal Bayesian Networks: A Gentle Introduction

Learning Bayesian networks: approaches and issues

“…These state that an effect is independent of its non-effects, given its direct causes and that the conditional independencies in the graph are equivalent to those in its probability distribution (see Druzdzel & Simon, 1993;Spirtes et al, 2000;Neapolitan, 2004;Huang & Valtorta, 2006;Valtorta & Huang, 2008 for more on these assumptions). It turns out that there are and these can be identified by a property known as d-separation, which is a purely graphical test, that is, a test that can be implemented by performing a search on a graph.…”

“…Finally, if it is assumed that in a Bayesian network, an arc from x to y means that x is a direct cause of y , then at least one of a number of causal assumptions is being made, such as the causal Markov assumption or the causal faithfulness assumption. These state that an effect is independent of its non-effects, given its direct causes and that the conditional independencies in the graph are equivalent to those in its probability distribution (see Druzdzel & Simon, 1993; Spirtes et al ., 2000; Neapolitan, 2004; Huang & Valtorta, 2006; Valtorta & Huang, 2008 for more on these assumptions). If this is the case, then this Bayesian network is capturing knowledge in a succinct way that is immediately obvious to humans, yet also with a well-understood formalism underlying the operations that can be performed.…”

A software system for causal reasoning in causal Bayesian networks

“…The algorithm is sound and complete even when the algorithm is used in a general causal graph, which has been proved by Huang and Valtorta. A similar result was provided by Shpitser and Pearl [17,22].…”

“…In the next chapter, we present the definitions and notations and lemmas used to support identify algorithms in this thesis. In chapter 3, three systematic procedures (identify causal effect of T on S, conditional causal effects of T [17].…”

“…v => and G (M 1 ) = G (M2) = G[17].The causal effect of a set of variables T on a disjoint set of variables S conditioned on another set C is said to be identifiable from a graph G if all the quantities ( | ) t P s c can be computed uniquely from any positive probability of the observed variables--that is,…”