Surrogate-Powered Inference: Regularization and Adaptivity
Abstract
High-quality labeled data are essential for reliable statistical inference, but are often limited by validation costs. While surrogate labels provide cost-effective alternatives, their noise can introduce non-negligible bias. To address this challenge, we propose the surrogate-powered inference (SPI) toolbox, a unified framework that leverages both the validity of high-quality labels and the abundance of surrogates to enable reliable statistical inference. SPI comprises three progressively enhanced versions. Base-SPI integrates validated labels and surrogates through augmentation to improve estimation efficiency. SPI+ incorporates regularized regression to safely handle multiple surrogates, preventing performance degradation due to error accumulation. SPI++ further optimizes efficiency under limited validation budgets through an adaptive, multiwave labeling procedure that prioritizes informative subjects for labeling. Compared to traditional methods, SPI substantially reduces the estimation error and increases the power in risk factor identification. These results demonstrate the value of SPI in improving the reproducibility. Theoretical guarantees and extensive simulation studies further illustrate the properties of our approach.
Summary
This paper addresses the problem of statistical inference when high-quality labeled data is scarce and expensive, but noisy surrogate labels are abundant. The authors propose a unified framework called Surrogate-Powered Inference (SPI) to leverage both types of data effectively. SPI has three versions: Base-SPI, SPI+, and SPI++. Base-SPI uses an augmented estimation approach to combine validated labels and surrogates. SPI+ builds on Base-SPI by incorporating regularized regression to handle multiple surrogates safely and prevent performance degradation due to error accumulation. SPI++ further optimizes efficiency under limited validation budgets by adaptively selecting informative subjects for labeling in a multiwave procedure. The paper demonstrates through simulations that SPI reduces estimation error and increases the power of risk factor identification compared to traditional methods. The authors also provide theoretical guarantees and an R package for the SPI toolbox. The framework matters because it offers a practical solution to improve statistical inference and reproducibility in scenarios where high-quality labels are costly to obtain.
Key Insights
- •Novel Framework: The SPI framework provides a unified approach to integrate validated labels and surrogate labels for improved statistical inference.
- •No-Harm Principle: SPI+ satisfies the "no-harm" principle, ensuring that incorporating surrogate information does not degrade estimation performance compared to using only validated labels.
- •Regularized Regression: SPI+ uses regularized regression (Lasso and Group Lasso) to mitigate error accumulation from high-dimensional surrogate information, making it robust to noisy surrogates.
- •Adaptive Labeling: SPI++ adaptively selects subjects for validation based on their expected information gain, optimizing efficiency under limited validation budgets.
- •Multiwave Labeling: The multiwave labeling strategy in SPI++ allows for iteratively refining the labeling rule with newly obtained labels.
- •Simulation Results: Simulations show that SPI consistently reduces MSE compared to baseline methods, especially when using multiple surrogates and adaptive labeling. For example, in the imbalanced response case, adaptive labeling increased the number of the minority class in the validation sample by approximately 42.3% and 43.6%.
- •Theoretical Guarantees: The paper provides theoretical guarantees for the asymptotic properties of the SPI estimators.
Practical Implications
- •Real-world Applications: SPI can be applied in various domains where high-quality labels are expensive, such as sentiment analysis, medical diagnosis using electronic health records (EHRs), and image recognition.
- •Benefit to Practitioners/Engineers: Practitioners and engineers can use the SPI toolbox (R package) to improve the efficiency and accuracy of statistical inference in their applications by leveraging surrogate labels and adaptive labeling strategies.
- •Future Research Directions: The paper opens up several future research directions, including extending SPI to handle noisy covariates, high-dimensional settings, multi-task learning, and exploring tighter integration of human and machine intelligence.