Turn a loss function into an accuracy function

Question

I have the RMSE loss, defined as:

RMSE = np.sum(np.sqrt((np.array(pred_df.real_values) - np.array(pred_df.estimate_values))**2))

where the real values and predictions are between 0.0 and 5.0.

I want to use this as an accuracy metric, not as a loss, however I don't know the interval in which this function takes values. The only thing I can think of is that:

Worse case - all predictions are wrong (all are 5.0 apart): RMSE = 5.0 * len(pred_df) Best case - all predictions are correct: RMSE = 0.0

Can I just use RMSE - 5.0 * len(pred_df) as my accuracy metric? Is there a smarter way of doing this?

Answer 1

Actually, your loss is more of an TRSE as you are taking the root first then the total sum instead of mean, hence the "total root squared error":). If you really want RMSE loss,

RMSE = np.sqrt(np.mean((np.array(pred_df.real_values) - np.array(pred_df.estimate_values))**2))

To convert this to accuracy metric, you are correct in finding the min/max values but you should not be subtracting by max value; you should first subtract the min value and then divide by the difference of max and min values ie min-max normalization. This will give values in the range [0, 1] . The min value of RMSE is 0 and the max value is 5 (your best/worst case approach justifies this). Then, (RMSE - 0) / (5 - 0) = RMSE / 5 is the accuracy metric: acc = RMSE / 5