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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
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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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