Root Mean Squared Logarithmic Error (Rmsle)

[!def] Root Mean Squared Logarithmic Error (RMSLE)
$$
RMSLE = \frac{1}{N} \sum_i \sqrt{(log(y_i + 1) - log(\hat{y_i} + 1))^2}
$$

Pros:

1. Good at Handling Outliers

Cons:

1. Biased penalty
   1. Penalizes underestimation more than the overestimation