Huber Loss and Robust Location

The textbook Huber loss function provides a robust alternative to squared error when estimating location. It applies a quadratic penalty for small residuals and a linear penalty for large ones. This ensures that while small errors are treated efficiently like the mean, outliers do not exert unbounded influence on the estimate, as their gradients are clipped.

Experiment

Interact with the module at Huber Loss and Robust Location to see how outliers influence the loss and gradient.

1. Set Outlier to 10. Notice that the Huber loss curve transitions from quadratic to linear, bounding the influence of the outlier on the gradient.
2. Change the Location to 1. Observe how the residuals shift and how the gradients adjust to reflect the new location.
3. Adjust Delta to 2. The region where the loss acts quadratically is widened, increasing the influence of points that were previously outside the threshold.