MSLE - Mean Squared Logarithmic Error

\[\text{MSLE}(y, \hat{y}) = \frac{1}{N} \sum_{i=0}^{N - 1} (\log_e (1 + y_i) - \log_e (1 + \hat{y}_i) )^2\]

Where \(\log_e (x)\) means the natural logarithm of x. This metric is best to use when targets having exponential growth, such as population counts, average sales of a commodity over a span of years etc. Note that this metric penalizes an under-predicted estimate greater than an over-predicted estimate.

• Best possible score is 0.0, smaller value is better. Range = [0, +inf)

Latex equation code:

\text{MSLE}(y, \hat{y}) = \frac{1}{N} \sum_{i=0}^{N - 1} (\log_e (1 + y_i) - \log_e (1 + \hat{y}_i) )^2

Example to use MSLE metric: