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2022

Theory of Machine Learning with Limited Data

Sapir, Marina

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Application of machine learning may be understood as deriving new knowledge for practical use through explaining accumulated observations, training set.

Peirce used the term abduction for this kind of inference.
Here I formalize the concept of abduction for real valued hypotheses, and show that 14 of the most popular textbook ML learners (every learner I tested), covering classification, regression and clustering, implement this concept of abduction inference.
The approach is proposed as an alternative to statistical learning theory, which requires an impractical assumption of indefinitely increasing training set for its justification.

Theory of Machine Learning with Limited Data · Around

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Abduction and induction
C.S. Pierce · 1955
Earlier work this paper cites.
A training algorithm for optimal margin classifiers
B.E. Boser, I. M. Guyon, and V.N. Vapnik · 1992
Earlier work this paper cites.
The Essential Peirce, Volume 1
C.S. Peirce · 1992
Earlier work this paper cites.
The complexity of logic-based abduction
Thomas Eiter and Georg Gottlob · 1993
Earlier work this paper cites.
Support vector networks
C. Cortes and V. Vapnik · 1995
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