When would you use MSLE (mean squared log error) instead of MSE?

hard

Answer

$(\operatorname{log}(1 + y)\; - \;\operatorname{log}(1 + y_{\mathrm{hat}}))2$
$Penalizes relative errors instead of absolute ones — an error of 10 units when y=1000 is treated the same as an error of 1 unit when y=100.$
$Use when the target spans many orders of magnitude (population sizes, incomes, energy consumption).$
$Requires y \geq 0.$
$Also under-penalizes over-prediction less than under-prediction — biased slightly toward higher predictions.$
$RMSLE (square root) is more interpretable.$

Check yourself — multiple choice

MSLE penalizes absolute errors more than MSE
MSLE penalizes relative errors — good for targets spanning many orders of magnitude
Same as MAPE
MSLE requires negative targets

MSLE = MSE on $\operatorname{log}(1 + y)$ — relative errors, needs y ≥ 0. RMSLE is more interpretable.

#metrics-regression

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