Bishop 1995 Neural Networks
To explain why resampling and ensembles are so useful, it is helpful to formulate the neural network training process in statistical terms (Bishop, 1995). We regard the problem as that of estimating an unknown nonlinear function, which has additive noise, on the basis of a limited data set of examples, D. There are several sources of error in our neural network's predictions. First, and unavoidably, even a "perfect" network that exactly modeled the underlying function would make errors due to the noise. However, there is also error due to the fact that we need to fit the neural network model using the finite sample data set, D. This remaining error can be split into two components, the model bias and variance. The bias is the average error that a particular model training procedure will make across different particular data sets (drawn from the unknown function's distribution). The variance reflects the sensitivity of the modeling procedure to a particular choice of data set.
We can trade off bias versus variance. At one extreme, we can arbitrarily select a function that entirely ignores the data. This has zero variance, but presumably high bias, since we have not actually taken into account the known aspects of the problem at all. At the opposite extreme, we can
Source: Pattern Recognition Lab
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