El Error Cuadrático Logarítmico Medio (MSLE) es un función de pérdida 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 fórmula para MSLE puede expresarse como:
MSLE = (1/n) * Σ (log(1 + y_true) – log(1 + y_pred))²
donde:
- y_true representa los valores reales.
- y_pred representa los valores predichos.
- n es el número de observaciones.
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 o donde la escala de los datos varía ampliamente.
MSLE también tiene ventajas en 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 rendimiento del modelo. In practice, MSLE is often preferred over Error cuadrático medio (MSE) when dealing with exponential growth scenarios or when the predictions are expected to be on a logarithmic scale.