MAE / L1 normalization

This is loss metric for machine learning models.
It has different names:

• Mean absolute error
• Mean absolute difference
• L1 normalization (math jargon)

Computing MAE

To compute MAE we need to:

• calculate absolute difference between predictions and real values.
• compute average of it.

Total absolute error: 21
Mean absolute error: 7

Why absolute values?

If we compute non absolute difference, then negative errors can cancel out positive errors:

Total error: 0
Mean error: 0

Python code to compute MAE from scratch

def mae(predictions, targets):
    # Calculate the absolute differences
    absolute_differences = [abs(p - t) for p, t in zip(predictions, targets)]

    # Calculate the mean of the absolute differences
    mean_absolute_error = sum(absolute_differences) / len(absolute_differences)

    return mean_absolute_error

# Example usage
predictions = [3.0, 5.0, 2.5, 6.0]
targets = [3.5, 4.5, 2.0, 5.0]
result = mae(predictions, targets)
print("MAE:", result)

Python code to compute MAE with PyTorch

F.l1_loss(predictions, targets)

 Module torch.nn.functional, which the PyTorch team recommends importing as F

Math formula

$$\text{MAE} = \frac{1}{n} \sum_{i=1}^{n} |y_i – \hat{y}_i|$$

Specifics

Doesn’t have such strong punishment for big differences as RMSE / L2 normalization
MAE is used less frequently than RMSE / L2 normalization