Mean Squared Logarithmic Error (Msle)

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

Pros:

1. Good at Handling Outliers

Cons:

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