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Monotonicity: Theory and Implementation

Sill, Joseph and Abu-Mostafa, Yaser (1997) Monotonicity: Theory and Implementation. In: Intelligent Methods in Signal Processing and Communications. Springer , Boston, MA, pp. 129-146. ISBN 978-1-4612-7383-7.

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We present a systematic method for incorporating prior knowledge (hints) into the learning-from-examples paradigm. The hints are represented in a canonical form that is compatible with descent techniques for learning. We focus in particular on the monotonicity hint, which states that the function to be learned is monotonic in some or all of the input variables. The application of monotonicity hints is demonstrated on two real-world problems-a credit card application task, and a problem in medical diagnosis. We report experimental results which show that using monotonicity hints leads to a statistically significant improvement in performance on both problems. Monotonicity is also analyzed from a theoretical perspective. We consider the class M of monotonically increasing binary output functions. Necessary and sufficient conditions for monotonic separability of a dichotomy are proven. The capacity of M is shown to depend heavily on the input distribution.

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Additional Information:© 1997 Birkhäuser Boston. The authors thank Eric Bax, Zehra Cataltepe, Malik Magdon-Ismail, and Xubo Song for many useful comments.
Subject Keywords:Input Vector; Decision Boundary; Test Error; Input Distribution; Monotonicity Constraint
Record Number:CaltechAUTHORS:20190710-141334973
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97034
Deposited By: Tony Diaz
Deposited On:10 Jul 2019 21:25
Last Modified:16 Nov 2021 17:25

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