What is Root Mean Square Error?

Root mean square error or root mean square deviation is one of the most commonly used measures for evaluating the quality of predictions. It shows how far predictions fall from measured true values using Euclidean distance.

To compute RMSE, calculate the residual (difference between prediction and truth) for each data point, compute the norm of residual for each data point, compute the mean of residuals and take the square root of that mean. RMSE is commonly used in supervised learning applications, as RMSE uses and needs true measurements at each predicted data point.

Root mean square error can be expressed as

RMSE formula

where N is the number of data points, y(i) is the i-th measurement, and y ̂(i) is its corresponding prediction.

Note: RMSE is NOT scale invariant and hence comparison of models using this measure is affected by the scale of the data. For this reason, RMSE is commonly used over standardized data.


Why is Root Mean Square Error (RMSE) Important?

In machine learning, it is extremely helpful to have a single number to judge a model’s performance, whether it be during training, cross-validation, or monitoring after deployment. Root mean square error is one of the most widely used measures for this. It is a proper scoring rule that is intuitive to understand and compatible with some of the most common statistical assumptions.

Note: By squaring errors and calculating a mean, RMSE can be heavily affected by a few predictions which are much worse than the rest. If this is undesirable, using the absolute value of residuals and/or calculating median can give a better idea of how a model performs on most predictions, without extra influence from unusually poor predictions.


How C3 AI Helps Organizations Use Root Mean Square Error (RMSE)

The C3 AI platform provides an easy way to automatically calculate RMSE and other evaluation metrics as part of a machine learning model pipeline. This extends into automated machine learning, where C3 AI® MLAutoTuner can automatically optimize hyperparameters and select model based on RMSE or other measures.