L'erreur logarithmique quadratique moyenne (MSLE) est une fonction de perte commonly used in regression tasks, particularly when the target variable can vary across several orders of magnitude. MSLE is defined as the average of the squared differences between the logarithmic values of the predicted and actual values.
La formule de la MSLE peut être exprimée comme :
MSLE = (1/n) * Σ (log(1 + y_true) – log(1 + y_pred))²
où :
- y_true représente les valeurs réelles.
- y_pred représente les valeurs prédites.
- n est le nombre d'observations.
By taking the logarithm of the values, MSLE can effectively handle skewed distributions and is particularly useful in cases where we want to penalize underestimations more than overestimations. This property makes MSLE suitable for situations where the predicted values can be zero ou lorsque l'échelle des données varie considérablement.
MSLE présente également des avantages dans interpretability, as it measures the relative difference between the actual and predicted values. A lower MSLE indicates a better fit of the model to the data, while a higher MSLE signifies a poorer performance du modèle. In practice, MSLE is often preferred over Erreur quadratique moyenne (MSE) when dealing with exponential growth scenarios or when the predictions are expected to be on a logarithmic scale.