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.

翻译：我们提出了一个基于Fisher线性判别（FLD）的领域自适应模型类。该类模型是两种假设的凸组合：i) 代表先前所见源任务的平均假设，与ii) 在新目标任务上训练的假设。针对特定的生成式设定，我们在0-1损失下推导出两种模型的最优凸组合，提出可计算的近似方案，并研究不同参数设置对最优假设、假设i)和假设ii)之间相对风险的影响。我们通过基于脑电图（EEG）和心电图（ECG）的分类实验验证了所提最优分类器的有效性，并论证该最优分类器可在不访问任何单个源任务直接信息的情况下完成计算。最后，我们讨论了进一步应用、局限性及未来可能的研究方向。