Near-optimal Bayesian Active Learning with Correlated and Noisy Tests
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by
Yuxin Chen, S. Hamed Hassani, Andreas Krause
2016
Abstract
We consider the Bayesian active learning and experimental design problem,
where the goal is to learn the value of some unknown target variable through a
sequence of informative, noisy tests. In contrast to prior work, we focus on
the challenging, yet practically relevant setting where test outcomes can be
conditionally dependent given the hidden target variable. Under such
assumptions, common heuristics, such as greedily performing tests that maximize
the reduction in uncertainty of the target, often perform poorly. In this
paper, we propose ECED, a novel, computationally efficient active learning
algorithm, and prove strong theoretical guarantees that hold with correlated,
noisy tests. Rather than directly optimizing the prediction error, at each
step, ECED picks the test that maximizes the gain in a surrogate objective,
which takes into account the dependencies between tests. Our analysis relies on
an information-theoretic auxiliary function to track the progress of ECED, and
utilizes adaptive submodularity to attain the near-optimal bound. We
demonstrate strong empirical performance of ECED on two problem instances,
including a Bayesian experimental design task intended to distinguish among
economic theories of how people make risky decisions, and an active preference
learning task via pairwise comparisons.
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