Unprovability comes to machine learning

Machine learning is concerned with the design and analysis of algorithms that can learn and improve their performance as they are exposed to data.

These modern real-world applications trace their origins to a subfield of machine learning that is concerned with the careful formalization and mathematical analysis of various machine-learning settings.

The goal of learning a predictor from a database of random examples was formalized in the aptly named probably approximately correct learning model7.

These are only a few examples of the many models used in machine learning.

EMX is actually quite similar to the PAC model, but the slightly different learning criterion surprisingly connects it to the continuum hypothesis and brings unprovability into the picture.

The authors’ proof involves a beautiful connection between machine learning and data compression that was first observed10 in the 1980s.

Machine learning has matured as a mathematical discipline and now joins the many subfields of mathematics that deal with the burden of unprovability and the unease that comes with it.

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