Approximately optimal domain adaptation with Fisher's Linear Discriminant

TL;DR

This paper introduces a Fisher's Linear Discriminant-based model for domain adaptation that optimally combines source and target hypotheses, demonstrating effectiveness in biomedical classification tasks without needing source data.

Contribution

It develops a novel convex combination approach for FLD in domain adaptation, deriving an optimal model under 0-1 loss and showing its practical effectiveness.

Findings

Optimal classifier improves target task accuracy

Effective without access to source task data

Applicable to EEG and ECG classification

Abstract

We propose a class of models based on Fisher's Linear Discriminant (FLD) in the context of domain adaptation. The class is the convex combination of two hypotheses: i) an average hypothesis representing previously seen source tasks and ii) a hypothesis trained on a new target task. For a particular generative setting we derive the optimal convex combination of the two models under 0-1 loss, propose a computable approximation, and study the effect of various parameter settings on the relative risks between the optimal hypothesis, hypothesis i), and hypothesis ii). We demonstrate the effectiveness of the proposed optimal classifier in the context of EEG- and ECG-based classification settings and argue that the optimal classifier can be computed without access to direct information from any of the individual source tasks. We conclude by discussing further applications, limitations, and possible future directions.