CRMSE: Compositional Root Mean Square Error Explained

CRMSE (Compositional Root Mean Square Error) is a common metric for evaluating the accuracy of regression models, particularly when dealing with compositional data. It measures the error between predicted and actual values, similar to Root Mean Square Error (RMSE), but with an added consideration for the nature of compositional data.

To calculate CRMSE, the difference between the target variable (y_train) and the predicted values (target_values) is first calculated (y_train - target_values). These differences are then squared ((y_train - target_values)**2), and their mean is computed (np.mean((y_train - target_values)**2)). Finally, the square root of this average is taken (np.sqrt(...)) to obtain the CRMSE.

CRMSE is particularly relevant when working with compositional data, which refers to data representing parts of a whole and summing up to 1 or 100%. In these cases, data is often log-transformed before applying RMSE.

The average of the squared differences provides a measure of the overall error between the predicted and true values. Taking the square root brings the error measurement back to the same unit as the original data, making it easier to interpret. This allows us to understand the model's performance in a more intuitive way, as it's aligned with the scale of the target variable.

It's important to note that a NaN (Not a Number) CRMSE value can occur if the differences are extremely small. This could indicate excellent model performance, but it could also suggest limited predictive power. Therefore, it's crucial to consider CRMSE alongside other metrics and domain knowledge to comprehensively assess the model's performance.