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The problem of estimating the Kullback-Leibler divergence D(P‖Q) between two unknown distributions P and Q is studied, under the assumption that the alphabet size k of the distributions can scale to infinity. The estimation is based on m independent samples drawn from P and n independent samples drawn from Q. It is first shown that there does not exist any(More)
The problem of estimating the KL divergence between two unknown distributions is studied. The alphabet size k of the distributions can scale to infinity. The estimation is based on m and n independent samples respectively drawn from the two distributions. It is first shown that there does not exist any consistent estimator to guarantee asymptotic small(More)
The following detection problem is studied, in which there are M sequences of samples out of which one outlier sequence needs to be detected. Each typical sequence contains n independent and identically distributed (i.i.d.) continuous observations from a known distribution π, and the outlier sequence contains n i.i.d. observations from an outlier(More)
We study a universal outlying sequence detection problem, in which there are M sequences of samples out of which a small subset of outliers need to be detected. A sequence is considered as an outlier if the observations therein are generated by a distribution different from those generating the observations in the majority of the sequences. In the universal(More)
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