Active Structure Learning of Bayesian Networks in an Observational Setting
This work addresses the problem of efficient Bayesian network learning for researchers in machine learning and statistics, offering incremental improvements in sample efficiency under specific conditions.
The paper tackles active structure learning of Bayesian networks under observational constraints by proposing a new algorithm that achieves with high probability a structure score within ε of optimal, demonstrating sample complexity reductions up to a factor of Ω̃(d³) for stable distributions while matching baseline performance in worst-case scenarios.
We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint distribution of the network variables, and the algorithm iteratively selects which variables to observe in the next sample. We propose a new active learning algorithm for this setting, that finds with a high probability a structure with a score that is $ε$-close to the optimal score. We show that for a class of distributions that we term stable, a sample complexity reduction of up to a factor of $\widetildeΩ(d^3)$ can be obtained, where $d$ is the number of network variables. We further show that in the worst case, the sample complexity of the active algorithm is guaranteed to be almost the same as that of a naive baseline algorithm. To supplement the theoretical results, we report experiments that compare the performance of the new active algorithm to the naive baseline and demonstrate the sample complexity improvements. Code for the algorithm and for the experiments is provided at https://github.com/noabdavid/activeBNSL.