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Robust Learning of Fixed-Structure Bayesian Networks
We investigate the problem of learning Bayesian networks in a robust model
where an -fraction of the samples are adversarially corrupted. In
this work, we study the fully observable discrete case where the structure of
the network is given. Even in this basic setting, previous learning algorithms
either run in exponential time or lose dimension-dependent factors in their
error guarantees. We provide the first computationally efficient robust
learning algorithm for this problem with dimension-independent error
guarantees. Our algorithm has near-optimal sample complexity, runs in
polynomial time, and achieves error that scales nearly-linearly with the
fraction of adversarially corrupted samples. Finally, we show on both synthetic
and semi-synthetic data that our algorithm performs well in practice
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