@incollection{icml2020_6395,
abstract = {We study the problem of efficiently estimating the effect of an intervention on a single variable using observational samples. Our goal is to give algorithms with polynomial time and sample complexity in a non-parametric setting.
Tian and Pearl (AAAI \textquotesingle 02) have exactly characterized the class of causal graphs for which causal effects of atomic interventions can be identified from observational data. We make their result quantitative. Suppose 𝒫 is a causal model on a set V of n observable variables with respect to a given causal graph G, and let do(x) be an identifiable intervention on a variable X. We show that assuming that G has bounded in-degree and bounded c-components and that the observational distribution satisfies a strong positivity condition:
(i) [Evaluation] There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P\^{} that satisfies TV(P(V \vert do(x)), P\^{}(V)) < eps using m=O\textasciitilde (n/eps\^{}2) samples from P and O(mn) time. The evaluator can return in O(n) time the probability P\^{}(v) for any assignment v to V.
(ii) [Sampling] There is an algorithm that outputs with probability 2/3 a sampler for a distribution P\^{} that satisfies TV(P(V \vert do(x)), P\^{}(V)) < eps using m=O\textasciitilde (n/eps\^{}2) samples from P and O(mn) time. The sampler returns an iid sample from P\^{} with probability 1-delta in O(n log(1/delta)/eps) time.
We extend our techniques to estimate P(Y \vert do(x)) for a subset Y of variables of interest. We also show lower bounds for the sample complexity, demonstrating that our sample complexity has optimal dependence on the parameters n and eps as well as the strong positivity parameter.},
author = {Bhattacharyya, Arnab and Gayen, Sutanu and Kandasamy, Saravanan and Maran, Ashwin and Variyam, Vinodchandran N.},
booktitle = {Proceedings of Machine Learning and Systems 2020},
pages = {11144--11155},
title = {Learning and sampling of atomic interventions from observations},
year = {2020}
}