Efficient inference of interventional distributions

Abstract

We consider the problem of efficiently inferring interventional distributions in a causal Bayesian network from a finite number of observations. Let P be a causal model on a set V of observable variables on a given causal graph G. For sets X, Y ⊆ V, and setting x to X, let P x (Y) denote the interventional distribution on Y with respect to an intervention x to variables X. Shpitser and Pearl (AAAI 2006), building on the work of Tian and Pearl (AAAI 2001), gave an exact characterization of the class of causal graphs for which the interventional distribution P x (Y) can be uniquely determined.We give the first efficient version of the Shpitser-Pearl algorithm. In particular, under natural assumptions, we give a polynomial-time algorithm that on input a causal graph G on observable variables V, a setting x of a set X ⊆ V of bounded size, outputs succinct descriptions of both an evaluator and a generator for a distribution P that is ε-close (in total variation distance) toWe also show that when Y is an arbitrary set, there is no efficient algorithm that outputs an evaluator of a distribution that is ε-close to P x (Y) unless all problems that have statistical zero-knowledge proofs, including the Graph Isomorphism problem, have efficient randomized algorithms.

Causal Structure Learning: a Combinatorial Perspective

“…Introducing interventional data opens possibilities for reductions in overall sample complexity and a further landscape of tradeoffs between interventional and observational sample complexities. Indeed, interventional data has been considered in recent works [1,17] on the statistical and computational complexity of causal inference tasks, where the causal graph is assumed to be known and the task is to estimate interventional distributions. An interesting future direction is to also explore the effect of interventional data on the complexity of causal structure learning.…”

Causal Structure Learning: A Combinatorial Perspective

“…Incorporating interventional data into these analyses would open the possibility for a reduction in overall sample complexity, and may introduce a landscape of trade-offs between interventional and observational sample complexities. Indeed, interventional data has been considered in recent works [1,17] on the statistical and computational complexity of causal inference tasks, where the causal graph is assumed to be known and the task is to estimate interventional distributions. An interesting future direction is to also explore the effect of interventional data on the complexity of causal structure learning.…”