标题： 无监督最优深度迁移学习在一般条件转移下的分类 显示英文标题

标题： Unsupervised optimal deep transfer learning for classification under general conditional shift

摘要： 仅在标记的源数据上训练的分类器在应用于来自不同分布的未标记目标数据时可能会产生误导性结果。 迁移学习可以通过将知识从源数据转移到目标数据来纠正这一点，但其效果通常依赖于严格的假设，例如标签偏移。 在本文中，我们引入了一个新颖的通用条件偏移（GCS）假设，其中包含标签偏移作为一个特殊场景。 在GCS下，我们证明了目标分布和偏移函数都是可识别的。 为了估计源数据的条件概率${\bm\eta}_P$，我们提出利用深度神经网络（DNN）。 在转移DNN估计器之后，我们利用伪最大似然方法估计目标标签分布${\bm\pi}_Q$。 最终，通过结合这些估计并避免估计偏移函数的需求，我们构建了我们提出的贝叶斯分类器。 我们在${\bm\eta}_P$的内在维度方面建立了对${\bm\eta}_P$和${\bm\pi}_Q$的估计量的浓度界限。 值得注意的是，我们的基于DNN的分类器达到了最优最小最大速率，最多相差一个对数因子。 我们方法的一个关键优势是当${\bm\eta}_P$展现出低维结构时，能够有效应对维度灾难。 数值模拟以及对阿尔茨海默病数据集的分析突显了其卓越的性能。 显示英文摘要

摘要： Classifiers trained solely on labeled source data may yield misleading results when applied to unlabeled target data drawn from a different distribution. Transfer learning can rectify this by transferring knowledge from source to target data, but its effectiveness frequently relies on stringent assumptions, such as label shift. In this paper, we introduce a novel General Conditional Shift (GCS) assumption, which encompasses label shift as a special scenario. Under GCS, we demonstrate that both the target distribution and the shift function are identifiable. To estimate the conditional probabilities ${\bm\eta}_P$ for source data, we propose leveraging deep neural networks (DNNs). Subsequent to transferring the DNN estimator, we estimate the target label distribution ${\bm\pi}_Q$ utilizing a pseudo-maximum likelihood approach. Ultimately, by incorporating these estimates and circumventing the need to estimate the shift function, we construct our proposed Bayes classifier. We establish concentration bounds for our estimators of both ${\bm\eta}_P$ and ${\bm\pi}_Q$ in terms of the intrinsic dimension of ${\bm\eta}_P$ . Notably, our DNN-based classifier achieves the optimal minimax rate, up to a logarithmic factor. A key advantage of our method is its capacity to effectively combat the curse of dimensionality when ${\bm\eta}_P$ exhibits a low-dimensional structure. Numerical simulations, along with an analysis of an Alzheimer's disease dataset, underscore its exceptional performance.