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：我们提出了一类基于Fisher线性判别（FLD）的领域自适应模型。该模型由两个假设的凸组合构成：i) 表示先前所见源任务的平均假设，以及ii) 针对新目标任务训练的假设。针对特定的生成式设置，我们推导了在0-1损失下两个模型的最优凸组合，提出了可计算的近似方法，并研究了不同参数设置对最优假设、假设i)和假设ii)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，并论证了在无需获取任何单个源任务直接信息的情况下即可计算出该最优分类器。最后，我们讨论了进一步的应用、局限性和可能的未来方向。