Geodesic
Discriminating between causal structures in Bayesian Networks given partial observations
Kybernetika, Tome 50 (2014) no. 2, pp. 284-295
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Given a fixed dependency graph $G$ that describes a Bayesian network of binary variables $X_1, \dots, X_n$, our main result is a tight bound on the mutual information $I_c(Y_1, \dots, Y_k) = \sum_{j=1}^k H(Y_j)/c - H(Y_1, \dots, Y_k)$ of an observed subset $Y_1, \dots, Y_k$ of the variables $X_1, \dots, X_n$. Our bound depends on certain quantities that can be computed from the connective structure of the nodes in $G$. Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.
Given a fixed dependency graph $G$ that describes a Bayesian network of binary variables $X_1, \dots, X_n$, our main result is a tight bound on the mutual information $I_c(Y_1, \dots, Y_k) = \sum_{j=1}^k H(Y_j)/c - H(Y_1, \dots, Y_k)$ of an observed subset $Y_1, \dots, Y_k$ of the variables $X_1, \dots, X_n$. Our bound depends on certain quantities that can be computed from the connective structure of the nodes in $G$. Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.
DOI : 10.14736/kyb-2014-2-0284
Classification : 60A08, 62-09, 62B09, 62H99
Keywords: Bayesian networks; causal Markov condition; information theory; information inequalities; common ancestors; causal inference 
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Moritz, Philipp; Reichardt, Jörg; Ay, Nihat. Discriminating between causal structures in Bayesian Networks given partial observations. Kybernetika, Tome 50 (2014) no. 2, pp. 284-295. doi: 10.14736/kyb-2014-2-0284

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