平均二乗対数誤差（MSLE）は 損失関数 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.
MSLEの式は次のように表されます：
MSLE = (1/n) * Σ (log(1 + y_true) – log(1 + y_pred))²
ただし：
- y_true 実測値を表します。
- y_pred 予測値を表します。
- n 観測数を表します。
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 または、データのスケールが大きく異なる場合に有効です。
MSLEには、また次のような利点もあります。 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 モデルのパフォーマンス. In practice, MSLE is often preferred over 平均二乗誤差 (MSE) when dealing with exponential growth scenarios or when the predictions are expected to be on a logarithmic scale.