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Monotonicity: Theory and
Joseph Sill
Yaser Abu­Mostafa
ABSTRACT We present a systematic method for incorporating prior
knowledge (hints) into the learning­from­examples paradigm. The hints
are represented in a canonical form that is compatible with descent tech­
niques 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 real­world 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 perfor­
mance 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 sepa­
rability of a dichotomy are proven. The capacity of M is shown to depend
heavily on the input distribution.


Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology


Collections: Computer Technologies and Information Sciences