Finite-State Extreme Effect Variable
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We generalize to the finite-state case the notion of the extreme effect variable Y that accumulates all the effect of a variant variable V observed in changes of another variable X. We conduct theoretical analysis and turn the problem of finding of an effect variable into a problem of a simultaneous decomposition of a set of distributions. The states of the extreme effect variable, on the one hand, are minimally affected by the variant variable V and, on the other hand, are extremely different with respect to the observable variable X. We apply our technique to online evaluation of a web search engine through A/B testing and show its utility.
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