Generalized Binary Search For SplitNeighborly Problems
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:15611569, 2018.
Abstract
In sequential hypothesis testing, Generalized Binary Search (GBS) greedily chooses the test with the highest information gain at each step. It is known that GBS obtains the gold standard query cost of O(log n) for problems satisfying the kneighborly condition, which requires any two tests to be connected by a sequence of tests where neighboring tests disagree on at most k hypotheses. In this paper, we introduce a weaker condition, splitneighborly, which requires that for the set of hypotheses two neighbors disagree on, any subset is splittable by some test. For four problems that are not kneighborly for any constant k, we prove that they are splitneighborly, which allows us to obtain the optimal O(log n) worstcase query cost.
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