Robust and flexible learning of a high-dimensional classification rule using auxiliary outcomes.

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Correlated outcomes are prevalent in various applications, with one often being of primary interest while others serve as auxiliary.
• Traditional multi-task learning (MTL) can introduce bias in target outcome estimation, particularly with model misspecification, by averaging losses across all outcomes.

Purpose of the Study:

• To develop a robust transfer learning method for estimating high-dimensional linear decision rules for a target outcome in the presence of auxiliary outcomes.
• To mitigate estimation bias inherent in traditional MTL approaches.

Main Methods:

• A novel robust transfer learning approach is proposed, decomposing estimation bias into within-subspace and against-subspace components.
• The method integrates a multi-task learning (MTL) step utilizing all outcomes for enhanced efficiency.
• A subsequent calibration step employs only the outcome of interest to correct identified biases.

Main Results:

• The proposed method yields an estimator with lower estimation error compared to methods using only the target outcome.
• The approach effectively corrects for both within-subspace and against-subspace estimation biases.
• Simulations and real-world data analyses confirm the method's superior performance.

Conclusions:

• The developed robust transfer learning technique offers a significant improvement in estimating target outcomes when auxiliary correlated outcomes are available.
• This approach provides a more accurate and reliable estimation strategy than traditional MTL or single-outcome methods, especially in high-dimensional settings.