Active Learning is essential for more label-efficient deep learning. Bayesian Active Learning has focused on BALD, which reduces model parameter uncertainty. However, we show that BALD gets stuck on out-of-distribution or junk data that is not relevant for the task. We examine a novel *Expected Predictive Information Gain (EPIG)* to deal with distribution shifts of the pool set. EPIG reduces the uncertainty of *predictions* on an unlabelled *evaluation set* sampled from the test data distribution whose distribution might be different to the pool set distribution. Based on this, our new EPIG-BALD acquisition function for Bayesian Neural Networks selects samples to improve the performance on the test data distribution instead of selecting samples that reduce model uncertainty everywhere, including for out-of-distribution regions with low density in the test data distribution. Our method outperforms state-of-the-art Bayesian active learning methods on high-dimensional datasets and avoids out-of-distribution junk data in cases where current state-of-the-art methods fail.
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