[Link] Better results by changing Bayes’ theorem

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If it ever turns out that Bayes fails - receives systematically lower rewards on some problem, relative to a superior alternative, in virtue of its mere decisions - then Bayes has to go out the window.

-- Eliezer Yudkowsky, Newcomb's Problem and Regret of Rationality

Don't worry, we don't have to abandon Bayes’ theorem yet. But changing it slightly seems to be the winning Way given certain circumstances. See below:

In Peter Norvig’s talk The Unreasonable Effectiveness of Data, starting at 37:42, he describes a translation algorithm based on Bayes’ theorem. Pick the English word that has the highest posterior probability as the translation. No surprise here. Then at 38:16 he says something curious.

So this is all nice and theoretical and pure, but as well as being mathematically inclined, we are also realists. So we experimented some, and we found out that when you raise that first factor [in Bayes' theorem] to the 1.5 power, you get a better result.

In other words, if we change Bayes’ theorem (!) we get a better result. He goes on to explain

Link: johndcook.com/blog/2012/03/09/monkeying-with-bayes-theorem/

Peter Norvig - The Unreasonable Effectiveness of Data

If it ever turns out that Bayes fails - receives systematically lower rewards on some problem, relative to a superior alternative, in virtue of its mere decisions - then Bayes has to go out the window.

-- Eliezer Yudkowsky, Newcomb's Problem and Regret of Rationality

Don't worry, we don't have to abandon Bayes’ theorem yet. But changing it slightly seems to be the winning Way given certain circumstances. See below:

In Peter Norvig’s talk The Unreasonable Effectiveness of Data, starting at 37:42, he describes a translation algorithm based on Bayes’ theorem. Pick the English word that has the highest posterior probability as the translation. No surprise here. Then at 38:16 he says something curious.

So this is all nice and theoretical and pure, but as well as being mathematically inclined, we are also realists. So we experimented some, and we found out that when you raise that first factor [in Bayes' theorem] to the 1.5 power, you get a better result.

In other words, if we change Bayes’ theorem (!) we get a better result. He goes on to explain

Link: johndcook.com/blog/2012/03/09/monkeying-with-bayes-theorem/

Peter Norvig - The Unreasonable Effectiveness of Data

Any other machine learning algorithm is a potential example for the observation 'naive token-by-token Bayes can be outperformed'.

Any other machine learning algorithm is a potential example for the observation 'naive token-by-token Bayes can be outperformed'.

I see. I didn't know this was the case. I am sorry if this is something really banal, it was new to me. Feel free to downvote it.