DWMD：用于特定领域隐藏表示匹配的维度加权有序矩离散
DWMD: Dimensional Weighted Orderwise Moment Discrepancy for Domain-specific Hidden Representation Matching
摘要：
在无监督领域自适应（UDA）中，从源领域到不同但语义相关的目标领域的知识转移一直是一个重要的课题。该领域的一个关键挑战是建立一个度量标准，可以准确地测量两个同质域之间的数据分布差异，并采用它的分布对齐，特别是在隐藏的激活空间中的特征表示的匹配。现有的分布匹配方法在实际应用中既不能显式地按序对齐高阶矩，也不能满足某些假设的前提。我们提出了一种新的基于矩的概率分布度量称为维度加权有序矩差异（DWMD）的特征表示匹配的UDA方案。我们的度量函数利用了一系列高阶矩对齐，我们从理论上证明了我们的DWMD度量函数是无误差的，这意味着它可以严格反映域之间的分布差异，是有效的，没有任何特征分布假设。此外，由于每个特征维度中的概率分布之间的差异是不同的，因此在我们的函数中考虑了维度加权。我们进一步计算了DWMD度量的经验估计在实际应用中的误差界。在基准数据集上的综合实验表明，我们的方法产生了最先进的分布度量。
英文摘要：
Knowledge transfer from a source domain to a different but semantically related target domain has long been an important topic in the context of unsupervised domain adaptation (UDA). A key challenge in this field is establishing a metric that can exactly measure the data distribution discrepancy between two homogeneous domains and adopt it in distribution alignment, especially in the matching of feature representations in the hidden activation space. Existing distribution matching approaches can be interpreted as failing to either explicitly orderwise align higher-order moments or satisfy the prerequisite of certain assumptions in practical uses. We propose a novel moment-based probability distribution metric termed dimensional weighted orderwise moment discrepancy (DWMD) for feature representation matching in the UDA scenario. Our metric function takes advantage of a series for high-order moment alignment, and we theoretically prove that our DWMD metric function is error-free, which means that it can strictly reflect the distribution differences between domains and is valid without any feature distribution assumption. In addition, since the discrepancies between probability distributions in each feature dimension are different, dimensional weighting is considered in our function. We further calculate the error bound of the empirical estimate of the DWMD metric in practical applications. Comprehensive experiments on benchmark datasets illustrate that our method yields state-of-the-art distribution metrics.
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