Derive and implement calibration via temperature scaling

Q: Derive and implement calibration via temperature scaling

This is a Machine Learning interview question from NewsBreak for Machine Learning Engineer roles. View the full question and solution on PracHub.

Q: How do I approach Machine Learning interview questions?

Machine Learning questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master machine learning interviews.

Question

Temperature Scaling for Softmax Calibration

Context

You have a trained multi-class classifier that outputs logits z(x) ∈ R^K for input x (the classifier is fixed; only calibration is learned). Temperature scaling calibrates predicted probabilities as:

p_i(x; T) = softmax(z_i(x) / T)

where T > 0 is a single scalar temperature shared across classes and inputs.

You are given a held-out validation set with logits and true labels, and you must learn T by minimizing negative log-likelihood (NLL).

Task

Write the NLL on the validation set as a function of T.
Derive the gradient of this NLL with respect to T.
Implement Python code that learns T by minimizing this NLL (e.g., gradient descent), and provide a function that applies the learned T to calibrate new predictions.

Derive and implement calibration via temperature scaling

Temperature Scaling for Softmax Calibration

Context

Task

Solution (Locked)

Comments (0)