Transfer Learning for Linear Discriminant Analysis with a Shared Classification Signal

2026-07-09 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This paper introduces a transfer learning framework for high-dimensional linear discriminant analysis (LDA) in two-class classification, addressing scenarios with one target and multiple source domains. The core innovation is decomposing the mean difference in each domain into a deterministic common component, representing a shared classification signal, and a domain-specific random deviation. Under spiked covariance models, the research derives deterministic limits for the target-domain Gaussian-calibrated error of weighted transfer classifiers in both homogeneous and heterogeneous covariance settings. These limits quantify the impact of shared signals, domain-specific variations, dimension-to-sample-size ratios, and spike structures on transfer performance. The framework also yields oracle transfer weights, consistent data-driven plug-in estimators, and an asymptotically optimal correction for intercept bias caused by unbalanced target-domain class sample sizes. Empirical studies on ADHD-200 and PPMI biomedical datasets demonstrate superior classification accuracy compared to baseline methods.

Key takeaway

For research scientists developing high-dimensional classification models with limited target domain data, this work provides a robust framework. You should consider explicitly modeling shared classification signals across source and target domains using TLDA-O or TLDA-E, especially when dealing with spiked covariance structures. Implementing the proposed optimal transfer weights and intercept bias correction for unbalanced class sizes can significantly improve classification accuracy, as demonstrated on biomedical datasets like ADHD-200 and PPMI.

Key insights

Transfer learning for high-dimensional LDA benefits from explicitly modeling shared classification signals and correcting for class imbalance.

Principles

• Decompose mean differences into shared and domain-specific components.
• Optimal transfer weights depend on effective signal and variance costs.
• Unbalanced class sizes introduce correctable intercept bias.

Method

The method involves deriving deterministic limits for Gaussian-calibrated error under spiked covariance models, which then inform oracle transfer weights and data-driven plug-in estimators. It also includes an asymptotically optimal correction for intercept bias.

In practice

• Apply TLDA-O for homogeneous covariance structures across domains.
• Use TLDA-E for heterogeneous covariance structures in multi-site data.
• Implement intercept bias correction for unbalanced target-domain class sizes.

Topics

• Transfer Learning
• Linear Discriminant Analysis
• High-Dimensional Classification
• Spiked Covariance Models
• Multi-site Biomedical Data
• Class Imbalance Correction

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.