Mean squared logarithmic error (MSLE) is, as the name suggests, a variation of the Mean Squared Error. The loss is the mean over the seen data of the squared differences between the log-transformed true and predicted values, or writing it as a formula:

where ŷ is the predicted value.

This loss can be interpreted as a measure of the ratio between the true and predicted values, since:

mage::MSLE_02.png[Ratio between the true and predicted values]

The reason ‘1’ is added to both y and ŷ is for mathematical convenience since log(0)is not defined but both y or ŷ can be 0.