Universal Hypothesis Testing via Mismatched Divergence

Optimal solution to the universal hypothesis testing problem suffers from high variance for large alphabet distributions. We propose a new approach to this problem that addresses this issue. Our solution is based on the mismatched divergence which is a new lower bound on Kullback-Leibler divergence (i.e., relative entropy). We present results on the asymptotic statistics of our test statistic and geometry of our mismatched test.

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