Math Park - 11/01/2014 - Yann Ollivier, Mathematics, inductive reasoning and...

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Institut Henri Poincaré

Published on Mar 5, 2014
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Problems of inductive reasoning or extrapolation such as "guessing the sequence of a series of numbers", or more generally, "understanding the hidden structure in observations", are fundamental if we want to one day build artificial intelligence. One might have the impression that these problems are not mathematically well defined, but there is a rigorous mathematical theory of inductive reasoning and extrapolation, based on principles of computability theory. This theory was defined 50 years ago by Ray Solomonoff, but we are only beginning to have mathematical tools to apply it in practice, thanks to techniques of probability, data compression, differential geometry, information theory. We will give the first mathematical properties as well as some examples inspired by artificial intelligence.

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