Daily Archives: November 16, 2012

Same Chernoff

I’ve been reading up on the Chernoff face for data visualization, which, as I’ve mentioned, is so cute. This helped me demonstrate that I haven’t forgotten everything from my grad school days, like a bound with name similar to the face. Back in my olden days, I thought Chernoff bounds were the cutest, and Chernoff faces were quite far from what I spent my time on.

So what a nice continuity that I learned it was the same Chernoff who lent his name to both the bound and the face. He seems to have a good sense of humor about both, and says that a different Herman deserves credit for the bound:

My result, involving the infimum ofa moment generating function, was less elegant and less general than the Cramer result, but did not require a special condition that Cramer required. Also, my proof could be described as crudely beating the problem to death. Herman claimed that he could get a lower bound much easier. I challenged him, and he produced a short Chebyshev Inequality type proof, which was so trivial that I did not trouble to cite his contribution.

What a mistake! It seems that Shannon had incorrectly applied the Central Limit theorem to the far tails of the distribution in one of his papers on Information theory. When his error was pointed out, he discovered the lower bound of Rubin in my paper and rescued his results. As a result I have gained great fame in electrical engineering circles for the Chernoff bound which was really due to Herman. One consequence of the simplicity of the proof was that no one ever bothered to read the original paper of which I was very proud. For years they referred to Rubin’s bound as the Chernov bound, not even spelling my name correctly. … Fortunately for me, my lasting fame, if any, will depend, not on Rubin’s bound, but on Chernoff faces.

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