document: Time and sample efficient discovery of Markov blankets and direct causal relations Data Mining with Bayesian Network learning has two important characteristics : under conditions learned edges between variables correspond to casual influences , and second , for every variable T in the network a special subset ( Markov Blanket ) identifiable by the network is the minimal variable set required to predict T. However , all known algorithms learning a complete BN do not scale up beyond a few hundred variables . On the other hand , all known sound algorithms learning a local region of the network require an exponential number of training instances to the size of the learned region . The contribution of this paper is two-fold . We introduce a novel local algorithm that returns all variables with direct edges to and from a target variable T as well as a local algorithm that returns the Markov Blanket of T. Both algorithms ( i ) are sound , ( ii ) can be run efficiently in datasets with thousands of variables , and ( iii ) significantly outperform in terms of approximating the true neighborhood previous state-of-the-art algorithms using only a fraction of the training size required by the existing methods . A fundamental difference between our approach and existing ones is that the required sample depends on the generating graph connectivity and not the size of the local region ; this yields up to exponential savings in sample relative to previously known algorithms . The results presented here are promising not only for discovery of local causal structure , and variable selection for classification , but also for the induction of complete BNs .
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