[Paper Review] Verified Uncertainty Calibration

Ananya Kumar, Percy Liang+1 more|arXiv (Cornell University)|Sep 23, 2019

Statistical Methods and Inference47 references85 citations

TL;DR

Introduces scaling-binning calibrator to achieve calibrated probabilities with favorable sample complexity, shows scaling methods underreport calibration error, and provides debiased estimators for calibration error with superior sample efficiency; validates on CIFAR-10 and ImageNet.

ABSTRACT

Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates---those representative of the true likelihood of a prediction. Most models are not calibrated out of the box but are recalibrated by post-processing model outputs. We find in this work that popular recalibration methods like Platt scaling and temperature scaling are (i) less calibrated than reported, and (ii) current techniques cannot estimate how miscalibrated they are. An alternative method, histogram binning, has measurable calibration error but is sample inefficient---it requires $O(B/ε^2)$ samples, compared to $O(1/ε^2)$ for scaling methods, where $B$ is the number of distinct probabilities the model can output. To get the best of both worlds, we introduce the scaling-binning calibrator, which first fits a parametric function to reduce variance and then bins the function values to actually ensure calibration. This requires only $O(1/ε^2 + B)$ samples. Next, we show that we can estimate a model's calibration error more accurately using an estimator from the meteorological community---or equivalently measure its calibration error with fewer samples ($O(\sqrt{B})$ instead of $O(B)$). We validate our approach with multiclass calibration experiments on CIFAR-10 and ImageNet, where we obtain a 35% lower calibration error than histogram binning and, unlike scaling methods, guarantees on true calibration. In these experiments, we also estimate the calibration error and ECE more accurately than the commonly used plugin estimators. We implement all these methods in a Python library: https://pypi.org/project/uncertainty-calibration

Motivation & Objective

• Motivate the need for probability calibration in critical applications (medicine, weather, NLP).
• Show limitations of common recalibration methods (Platt scaling, temperature scaling) in true calibration and error estimation.
• Propose a method that blends scaling with binning to achieve calibration with favorable sample complexity and measurable calibration error.
• Develop efficient estimators for calibration error, including a debiased estimator with reduced sample complexity.
• Empirically validate calibration performance and estimation accuracy on multiclass datasets (CIFAR-10, ImageNet).

Proposed method

• Propose scaling-binning calibrator that first fits a function g in a family G to recalibration data.
• Construct a uniform-mass binning scheme over the g(z) outputs to bin the transformed scores.
• Discretize by outputting the mean g(z) value per bin to obtain g_B and calibrate f via g_B∘f.
• Show theoretical calibration bound: CE(g_B) ≤ √(2)·min_g∈G CE(g) + ε under n ≥ c(B log B + log B / ε^2) samples.
• Demonstrate that binning g outputs yields lower calibration error than g alone (under certain conditions).
• Provide algorithms and proofs (sketch) for calibration guarantees and sample complexity improvements over histogram binning.

Experimental results

Research questions

• RQ1 Can scaling methods (Platt, temperature) reliably calibrate probabilities when true calibration error is difficult to measure?
• RQ2 Can we design a recalibration method that achieves both sample efficiency and verifiable calibration guarantees?
• RQ3 Does combining scaling with histogram-like binning (scaling-binning) yield better calibration error and measurability than existing methods?
• RQ4 How can calibration error be estimated more efficiently, especially in multiclass settings?
• RQ5 What is the impact of binning strategy on calibration error measurement and MSE?

Key findings

• Scaling-binning calibrator achieves calibration error lower than histogram binning in CIFAR-10 and ImageNet with B=100.
• The method requires O(1/ε^2 + B) samples to achieve calibration error ε, improving over histogram binning’s O(B/ε^2).
• Binned estimators enable efficient calibration error estimation with ˆE^2 measured within guarantees (ε-approximation).
• A debiased estimator reduces calibration-error estimation sample complexity from O(B) to O(√B).
• Experiments show 35% lower calibration error on CIFAR-10 and 5x lower calibration error on ImageNet (for B=100) compared to histogram binning; scaling methods do not provide true-calibration guarantees.
• The study provides an open-source Python library for uncertainty calibration at the provided URL.