Approximate medians and other quantiles in one pass and with limited memory
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Foundations of statistical natural language processing
Foundations of statistical natural language processing
Median bounds and their application
Journal of Algorithms
Relevance based language models
Proceedings of the 24th annual international ACM SIGIR conference on Research and development in information retrieval
A stochastic language model using dependency and its improvement by word clustering
COLING '98 Proceedings of the 17th international conference on Computational linguistics - Volume 2
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We point out that for two sets of measurements, it can happen that the average of one set is larger than the average of the other set on one scale, but becomes smaller after a non-linear monotone transformation of the individual measurements. We show that the inclusion of error bars is no safeguard against this phenomenon. We give a theorem, however, that limits the amount of “reversal” that can occur; as a by-product we get two non-standard one-sided tail estimates for arbitrary random variables which may be of independent interest. Our findings suggest that in the not infrequent situation where more than one cost measure makes sense, there is no alternative other than to explicitly compare averages for each of them, much unlike what is common practice.