We present a general theoretical and algorithmic analysis of the problem of multiple-source adaptation, a key learning problem in applications. We derive new normalized solutions with strong theoretical guarantees for the cross-entropy loss and other similar losses. We also provide new guarantees that hold in the case where the conditional probabilities for the source domains are distinct. We further present a novel analysis of the convergence properties of density estimation used in distribution-weighted combinations, and study their effects on the learning guarantees. Moreover, we give new algorithms for determining the distribution-weighted combination solution for the cross-entropy loss and other losses. We report the results of a series of experiments with real-world datasets. We find that our algorithm outperforms competing approaches by producing a single robust predictor that performs well on any target mixture distribution. Altogether, our theory, algorithms, and empirical results provide a full solution for the multiple-source adaptation problem with very practical benefits.

中文翻译：

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多源自适应理论与算法

我们提出了多源适应问题的一般理论和算法分析，这是应用中的一个关键学习问题。我们为交叉熵损失和其他类似损失推导出具有强有力理论保证的新的归一化解决方案。我们还提供了在源域的条件概率不同的情况下适用的新保证。我们进一步对分布加权组合中使用的密度估计的收敛特性进行了新的分析，并研究了它们对学习保证的影响。此外，我们给出了用于确定交叉熵损失和其他损失的分布加权组合解决方案的新算法。我们报告了一系列真实世界数据集实验的结果。我们发现我们的算法通过生成一个在任何目标混合分布上表现良好的单一稳健预测器来优于竞争方法。总而言之，我们的理论、算法和实证结果为多源适应问题提供了一个非常实用的解决方案。