I went straight to temperature scaling because it's the simplest and I could actually derive the optimization cleanly under time pressure.
Start by clarifying the requirements: the utility should fit a calibration map on a held-out set and then apply it to new logits. Discuss the trade-offs between temperature scaling, Platt scaling, and isotonic regression, and justify your choice based on data size and model output characteristics. Then outline the implementation steps, including fitting the calibrator and applying it to produce calibrated probabilities.
Pro tip: Emphasize that calibration should be evaluated on a separate validation set to avoid overfitting, and mention that temperature scaling is often preferred for neural networks due to its simplicity and effectiveness, but isotonic regression can be better with abundant data.
Confirm the input format (logits or probabilities), the size of the held-out set, and whether the task is binary or multiclass. Discuss the need for a separate calibration set.
Compare temperature scaling, Platt scaling, and isotonic regression in terms of assumptions, data requirements, and computational cost. Select one and justify.
Describe how to fit the chosen calibrator: for temperature scaling, optimize a single temperature parameter by minimizing NLL on the calibration set; for Platt scaling, fit a logistic regression on the logits; for isotonic regression, fit a non-decreasing function.
Write a function that takes new logits, applies the fitted calibration map, and returns calibrated probabilities (e.g., softmax with temperature, sigmoid with Platt parameters, or isotonic interpolation).
Assess calibration using metrics like Expected Calibration Error (ECE) or reliability diagrams on a validation set. Discuss potential pitfalls like overfitting and how to mitigate them.
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Reliability diagrams I knew cold, bucketing predictions and plotting mean confidence vs accuracy per bin.
Start by clearly defining reliability diagrams and ECE, then walk through the construction steps with attention to binning choices and their impact. Compare temperature scaling, Platt scaling, and isotonic regression in terms of flexibility, data requirements, and performance, and discuss trade-offs in the context of real-world deployment.
Pro tip: Emphasize that calibration should be evaluated on a held-out set and that the choice of binning scheme (e.g., equal-width vs. equal-frequency) can significantly affect ECE; mention that adaptive binning or kernel density estimators can provide more reliable estimates.
Explain that a reliability diagram plots predicted probability vs. observed accuracy, and ECE is the weighted average of the absolute difference between confidence and accuracy across bins.
Describe binning predictions (e.g., into 10 equal-width bins), computing the average confidence and accuracy per bin, and plotting them with the identity line for reference.
Detail the formula: ECE = sum over bins of (|B_m|/n) * |acc(B_m) - conf(B_m)|, and discuss how binning choices affect the result.
Discuss temperature scaling (single parameter, preserves accuracy, requires logits), Platt scaling (logistic regression on scores, works for binary/multiclass), and isotonic regression (non-parametric, flexible but prone to overfitting with limited data).
Highlight trade-offs: temperature scaling is simple and effective for neural networks but assumes a single temperature; Platt scaling is more flexible but can overfit; isotonic regression is highly flexible but needs lots of data and can produce non-monotonic calibrations. Mention evaluation on validation set and potential need for recalibration over time.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.