Detecting and Correcting for Label Shift with Black Box Predictors

Abstract: Faced with distribution shift between training and test set, we wish to detect and quantify the shift, and to correct our classifiers without test set labels. Motivated by medical diagnosis, where diseases (targets) cause symptoms (observations), we focus on label shift, where the label marginal $p(y)$ changes but the conditional $p(x| y)$ does not. We propose Black Box Shift Estimation (BBSE) to estimate the test distribution $p(y)$. BBSE exploits arbitrary black box predictors to reduce dimensionality prior to shift correction. While better predictors give tighter estimates, BBSE works even when predictors are biased, inaccurate, or uncalibrated, so long as their confusion matrices are invertible. We prove BBSE's consistency, bound its error, and introduce a statistical test that uses BBSE to detect shift. We also leverage BBSE to correct classifiers. Experiments demonstrate accurate estimates and improved prediction, even on high-dimensional datasets of natural images.

• The paper introduces Black Box Shift Estimation to detect label shift by leveraging the confusion matrix of arbitrary predictors.
• It provides theoretical guarantees such as consistency and error bounds, validated through experiments on datasets like MNIST and CIFAR-10.
• The approach corrects models via importance-weighted risk minimization, improving performance under shifted test distributions.

Detecting and Correcting for Label Shift with Black Box Predictors

Overview

The paper "Detecting and Correcting for Label Shift with Black Box Predictors" addresses the crucial problem of label shift in machine learning. Label shift occurs when the marginal distribution of labels, $p(y)$, changes between the training and test datasets while the conditional distribution $p(x|y)$ remains constant. This is particularly relevant in fields like medical diagnosis, where diseases (causes) generate observable symptoms (effects).

The authors propose a robust method called Black Box Shift Estimation (BBSE) to detect and correct label shifts. A key advantage of this method is its reliance on existing black box predictors, without requiring test set labels. The approach is versatile, accommodating predictors that may be biased or inaccurate, provided their confusion matrices are invertible.

Main Contributions

1. BBSE Methodology: BBSE estimates the test label distribution $q(y)$ by leveraging the confusion matrix obtained from an arbitrary black box predictor. The technique asserts consistency and error bounds, demonstrating its reliability.
2. Statistical Testing: BBSE is utilized to conduct a statistical test that determines the presence of label shift. The methodology encompasses a practical approach to detect distribution shifts using readily available test samples and predictor outputs.
3. Model Correction: By applying importance-weighted Empirical Risk Minimization, BBSE provides a way to adjust classifiers to perform accurately on shifted test data, even in high-dimensional datasets such as natural images.
4. Comparative Analysis: The paper rigorously benchmarks BBSE against other methods, such as Kernel Mean Matching (KMM), Expectation-Maximization (EM), and Bayesian inference, proving its efficacy across various scenarios.

Theoretical Insights

Underpinning their methodology, the authors offer extensive theoretical validation:

• Consistency: BBSE's estimates converge to the true test label distribution as the sample size increases, with proofs grounded in statistical theory.
• Error Bounds: They provide detailed convergence rates and conditions under which the estimators' errors decrease, highlighting the method's robustness across different predictor qualities.

Experiments and Results

The paper includes experimental validation on datasets like MNIST and CIFAR-10. It demonstrates:

• Detection and Correction: The BBSE approach effectively detects label shifts and corrects classifiers to match new data distributions. This is crucial for maintaining model accuracy amid changing data landscapes.
• Performance: Comparative experiments showcase the superiority of BBSE over traditional methods, particularly in scenarios with high-dimensional data or varying class distributions.

Implications and Future Directions

The proposed framework holds significant promise for practical applications where shifting distributions are common, such as real-time monitoring systems and adaptive diagnostic tools in healthcare.

• Real-World Applications: By integrating BBSE, models can dynamically adapt to changing environments with minimal human intervention, providing more reliable predictions.
• Further Research: The exploration of BBSE in streaming data contexts and the potential extension to other domain adaptation challenges represent promising avenues for future work.

In conclusion, this paper delivers a comprehensive approach to detecting and correcting label shifts using black box predictors, providing both theoretical foundations and practical solutions. It lays a solid groundwork for advancing domain adaptation methodologies in machine learning.