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Compressing multisets using tries
 IN INFORMATION THEORY WORKSHOP (ITW). IEEE, 2012
"... We consider the problem of efficient and lossless representation of a multiset of m words drawn with repetition from a set of size 2n. One expects that encoding the (unordered) multiset should lead to significant savings in rate as compared to encoding an (ordered) sequence with the same words, sin ..."
Abstract

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We consider the problem of efficient and lossless representation of a multiset of m words drawn with repetition from a set of size 2n. One expects that encoding the (unordered) multiset should lead to significant savings in rate as compared to encoding an (ordered) sequence with the same words, since information about the order of words in the sequence corresponds to a permutation. We propose and analyze a practical multiset encoder/decoder based on the trie data structure. The act of encoding requires O(m(n + logm)) operations, and decoding requires O(mn) operations. Of particular interest is the case where cardinality of the multiset scales as m = 1 c 2n for some c> 1, as n → ∞. Under this scaling, and when the words in the multiset are drawn independently and uniformly, we show that the proposed encoding leads to an arbitrary improvement in rate over encoding an ordered sequence with the same words. Moreover, the expected length of the proposed codes in this setting is asymptotically within a constant factor of 5 3 of the lower bound.
2011 IEEE Statistical Signal Processing Workshop (SSP) MULTILEVEL MINIMAX HYPOTHESIS TESTING
"... In signal detection, Bayesian hypothesis testing and minimax hypothesis testing represent two extremes in the knowledge of the prior probabilities of the hypotheses: full information and no information. We propose an intermediate formulation, also based on the likelihood ratio test, to allow for par ..."
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In signal detection, Bayesian hypothesis testing and minimax hypothesis testing represent two extremes in the knowledge of the prior probabilities of the hypotheses: full information and no information. We propose an intermediate formulation, also based on the likelihood ratio test, to allow for partial information. We partition the space of prior probabilities into a set of levels using a quantizationtheoretic approach with a minimax Bayes risk error criterion. Within each prior probability level, an optimal representative probability value is found, which is used to set the threshold of the likelihood ratio test. The formulation is demonstrated on signals with additive Gaussian noise. Index Terms — quantization, categorization, hypothesis testing, signal detection, Bayes risk error 1.