English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider testing and learning problems on causal Bayesian networks asdefined by Pearl (Pearl, 2009). Given a causal Bayesian network $\mathcal{M}$on a graph with $n$ discrete variables and bounded in-degree and bounded`confounded components', we show that $O(\log n)$ interventions on an unknowncausal Bayesian network $\mathcal{X}$ on the same graph, and$\tilde{O}(n/\epsilon^2)$ samples per intervention, suffice to efficientlydistinguish whether $\mathcal{X}=\mathcal{M}$ or whether there exists someintervention under which $\mathcal{X}$ and $\mathcal{M}$ are farther than$\epsilon$ in total variation distance. We also obtain sample/time/interventionefficient algorithms for: (i) testing the identity of two unknown causalBayesian networks on the same graph; and (ii) learning a causal Bayesiannetwork on a given graph. Although our algorithms are non-adaptive, we showthat adaptivity does not help in general: $\Omega(\log n)$ interventions arenecessary for testing the identity of two unknown causal Bayesian networks onthe same graph, even adaptively. Our algorithms are enabled by a newsubadditivity inequality for the squared Hellinger distance between two causalBayesian networks.

Learning and Testing Causal Models with Interventions