[Paper Review] Reliable Confidence Estimation via Online Learning.

Volodymyr Kuleshov, Stefano Ermon|arXiv (Cornell University)|Jul 13, 2016

Machine Learning and Data Classification3 citations

TL;DR

This paper proposes an online learning-based method for reliable confidence estimation in classification models by generating calibrated probabilities that remain accurate and well-calibrated even under distribution shift or adversarial inputs. The approach provides formal confidence bounds and operates without requiring a separate calibration dataset, ensuring theoretical guarantees on accuracy and convergence.

ABSTRACT

Assessing uncertainty within machine learning systems is an important step towards ensuring their safety and reliability. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e.g. when the data distribution differs from the one seen at training time. Here, we propose techniques that assess a classification algorithm's uncertainty via calibrated probabilities (i.e. probabilities that match empirical outcome frequencies in the long run) and which are guaranteed to be reliable (i.e. accurate and calibrated) on out-of-distribution input, including input generated by an adversary. Our methods admit formal bounds that can serve as confidence intervals, and process data in an online manner, which obviates the need for a separate calibration dataset. We establish theoretical guarantees on our methods' accuracies and convergence rates, and we validate them on two real-world problems: question answering and medical diagnosis from genomic data.

Motivation & Objective

• To address the failure of existing uncertainty estimation techniques when data distributions shift from training data.
• To develop a method that maintains reliable, calibrated probabilities on out-of-distribution and adversarial inputs.
• To eliminate the need for a separate calibration dataset by enabling online learning and real-time confidence estimation.
• To provide formal theoretical bounds on confidence intervals that are valid in the long run.
• To ensure robustness and accuracy of uncertainty estimates across diverse real-world applications such as question answering and genomic diagnosis.

Proposed method

• The method uses online learning to update model confidence estimates incrementally as new data arrives, avoiding batch processing and calibration data requirements.
• It generates calibrated probabilities that match empirical outcome frequencies over time, ensuring long-term reliability.
• The approach incorporates formal bounds on confidence intervals derived from statistical guarantees, enhancing interpretability and trust.
• It leverages a recursive estimation framework that adapts to data drift and distributional shifts in real time.
• The method is designed to be robust to adversarial examples by maintaining well-calibrated outputs even under perturbations.
• Theoretical analysis establishes convergence rates and accuracy bounds under minimal modeling assumptions.

Experimental results

Research questions

• RQ1 Can confidence estimation be made reliable under distribution shift without relying on a separate calibration dataset?
• RQ2 How can calibrated probabilities be maintained in online settings where data arrives sequentially?
• RQ3 To what extent do the proposed methods preserve accuracy and calibration on out-of-distribution and adversarial inputs?
• RQ4 What theoretical guarantees can be provided for confidence bounds in such online, distribution-shift-robust settings?
• RQ5 How do the methods perform in real-world applications with high-stakes uncertainty, such as medical diagnosis and question answering?

Key findings

• The proposed method achieves reliable confidence estimation even when test data distribution differs from training data.
• The approach maintains well-calibrated probabilities on adversarial inputs, demonstrating robustness to targeted perturbations.
• Formal confidence bounds are derived and shown to be valid under long-term empirical frequency matching.
• The method operates without requiring a separate calibration dataset, reducing data and infrastructure overhead.
• Empirical validation shows strong performance on real-world tasks, including question answering and genomic-based medical diagnosis.
• Theoretical analysis confirms convergence and accuracy guarantees under mild assumptions, supporting practical deployment.