On the Jensen-Shannon divergence and variational distance
We study the distance measures between two probability distributions via two different distance metrics, a new metric induced from Jensen-Shannon divergence, and the well known L/sub 1/ metric. We show that several important results and constructions in computational complexity under the L/sub 1/ me...
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| Veröffentlicht in: | IEEE transactions on information theory 2005-09, Vol.51 (9), p.3333-3336 |
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| container_title | IEEE transactions on information theory |
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| creator | TSAI, Shi-Chun TZENG, Wen-Guey WU, Hsin-Lung |
| description | We study the distance measures between two probability distributions via two different distance metrics, a new metric induced from Jensen-Shannon divergence, and the well known L/sub 1/ metric. We show that several important results and constructions in computational complexity under the L/sub 1/ metric carry over to the new metric, such as Yao's next-bit predictor, the existence of extractors, the leftover hash lemma, and the construction of expander graph based extractor. Finally, we show that the useful parity lemma in studying pseudorandomness does not hold in the new metric. |
| doi_str_mv | 10.1109/TIT.2005.853308 |
| format | Article |
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We show that several important results and constructions in computational complexity under the L/sub 1/ metric carry over to the new metric, such as Yao's next-bit predictor, the existence of extractors, the leftover hash lemma, and the construction of expander graph based extractor. 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| subjects | Applied sciences Complexity theory Computation Computational complexity Computer science Construction Divergence Exact sciences and technology expander Extractors Extraterrestrial measurements Graph theory Graphs Hash based algorithms Information systems Information theory Information, signal and communications theory Jensen-Shannon divergence leftover hash lemma Mutual information Parity parity lemma Probability Probability distribution Sampling methods Telecommunications and information theory |
| title | On the Jensen-Shannon divergence and variational distance |
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