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A metric is a function that outputs a distance between 2 elements of a set & meets certain strict criteria (some 'distance' functions are not metrics).

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Is there an error metric that decreases the weight when the target is near zero?

np.sqrt(np.mean((y_true - y_pred)**2 + w * np.exp(-np.abs(y_true)))) The cRMSE is a custom implementation of the Root Mean Squared Error (RMSE) error metric. … The cRMSE metric could be useful in cases where you want to give less weight to values close to zero, for example, in situations where predicting zero values accurately is considered less important than …