t14 - 4.5 Generalisation for Regression The problem of...

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Unformatted text preview: 4.5 Generalisation for Regression The problem of regression is that of finding a function which approximates mapping from an input domain to the real numbers based on a training sample. The fact that the output values are no longer binary means that the mismatch between the hypothesis output and its training value will no longer be discrete. We refer to the difference between the two values as the residual of the output, an indication of the accuracy of the fit at this point. We must decide how to measure the importance of this accuracy, as small residuals may be inevitable while we wish to avoid large ones. The loss function determines this measure. Each choice of loss function will result in a different overall strategy for performing regression. For example least squares regression uses the sum of the squares of the residuals. Although several different approaches are possible (see Section 4.8), we will provide an analysis for the generalisation performance of a regression function by using the bounds obtained for the classification case, as these will motivate the...
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