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Predictor Error Measures

  • Measure predictor accuracy: measure how far off the predicted value is from the actual known value
  • Loss function : measures the error betw. yi and the predicted value yi’
    • Absolute error: | yi – yi’|
    • Squared error: (yi – yi’)2

  • Test error (generalization error): the average loss over the test set

    Mean absolute error:

    \[\frac{\sum_{i=1}^{d}|y_{i}-y_{i}^{'}|}{d}\]

    Mean squared error:

    \[\frac{\sum_{i=1}^{d}(y_{i}-y_{i}^{'})^{2}}{d}\]

    Relative absolute error:

    \[\frac{\sum_{i=1}^{d}|y_{i}-y_{i}^{'}|}{\sum_{i=1}^{d}|y_{i}-\bar{y}|}\]

    Relative squared error:

    \[\frac{\sum_{i=1}^{d}(y_{i}-y_{i}^{'})^{2}}{\sum_{i=1}^{d}(y_{i}-\bar{y})^{2}}\]

    The mean squared-error exaggerates the presence of outliers 

    Popularly use (square) root mean-square error, similarly, root relative squared error

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