Bias variance Neural Networks
Feedforward neural networks trained by error backpropagation are examples of nonparametric regression estimators.The fundamental challenges in neural modeling are about representation rather than learning per se. Learning, as it is represented in some current neural networks, can be formulated as a (nonlinear) regression problem.The essence of the bias/variance dilemma lies in the fact that estimation error can be decomposed into two components, know as bias and variance; whereas incorrect models lead to high bias, truly model-free inference suffers from high variance. Thus, mode-free (tabula rasa) approaches to complex inference tasks are slot to "converge", in the sense that large training samples are required to achieve acceptable performance. This is the effect of high variance, and is a consequence of the large number of parameters, indeed infinite number in truly mode-free inference, that need to be estimated. Prohibitively large training sets are then required to reduce the variance contribution to estimation error. Parallel architectures and fast hardware do not help here: this "convergence problem" has to do with training set size rather than implementation. The only way to control the variance in complex inference problems is to use model-based inference is bias-prone: proper models are hard to identify for these more complex (and interesting) inference problems, and any model-based scheme is likely to be incorrect for the task at hand, that is highly biased.
Source: Troy's posterous
A principled approach for building and evaluating neural network classification models [An article from: Decision Support Systems]
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