Efficient agnostic learning of neural networks with bounded fan-in
Wee Sun Lee; Bartlett, P.L.; Williamson, R.C.
Information Theory, IEEE Transactions on
Volume 42, Issue 6, Nov 1996 Page(s):2118 - 2132
Digital Object Identifier 10.1109/18.556601
Summary:We show that the class of two-layer neural networks with bounded
fan-in is efficiently learnable in a realistic extension to the probably
approximately correct (PAC) learning model. In this model, a joint
probability distribution is assumed to exist on the observations and the
learner is required to approximate the neural network which minimizes
the expected quadratic error. As special cases, the model allows
learning real-valued functions with bounded noise, learning
probabilistic concepts, and learning the best approximation to a target
function that cannot be well approximated by the neural network. The
networks we consider have real-valued inputs and outputs, an unlimited
number of threshold hidden units with bounded fan-in, and a bound on the
sum of the absolute values of the output weights. The number of
computation steps of the learning algorithm is bounded by a polynomial
in 1/ε, 1/δ, n and B where ε is the desired accuracy,
δ is the probability that the algorithm fails, n is the input
dimension, and B is the bound on both the absolute value of the target
(which may be a random variable) and the sum of the absolute values of
the output weights. In obtaining the result, we also extended some
results on iterative approximation of functions in the closure of the
convex hull of a function class and on the sample complexity of agnostic
learning with the quadratic loss function
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