Lugosi, G.
Zeger, K.
Fac. of Electr. Eng., Tech. Univ. Budapest;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Jan 1996
Volume: 42,
Issue: 1
On page(s): 48-54
ISSN: 0018-9448
References Cited: 24
CODEN: IETTAW
INSPEC Accession Number: 5196852
Digital Object Identifier: 10.1109/18.481777
Posted online: 2002-08-06 20:16:49.0
Abstract
In pattern recognition or, as it has also been called, concept
learning, the value of a { 0,1}-valued random variable Y is to be
predicted based upon observing an Rd-valued random variable
X. We apply the method of complexity regularization to learn concepts
from large concept classes. The method is shown to automatically find a
good balance between the approximation error and the estimation error.
In particular, the error probability of the obtained classifier is shown
to decrease as O(√(logn/n)) to the achievable optimum, for large
nonparametric classes of distributions, as the sample size n grows. We
also show that if the Bayes error probability is zero and the Bayes rule
is in a known family of decision rules, the error probability is
O(logn/n) for many large families, possibly with infinite VC dimension
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