We revisit the problem of Domain Generalization (DG) where the hypotheses are composed of a common representation mapping followed by a labeling function. Popular DG methods optimize a well-known upper bound to the risk in the unseen domain. However, the bound contains a term that is not optimized due to its dual dependence on the representation mapping and the unknown optimal labeling function for the unseen domain. We derive a new upper bound free of the term having such dual dependence by imposing mild assumptions on the loss function and an invertibility requirement on the representation map when restricted to the low-dimensional data manifold. The derivation leverages old and recent transport inequalities that link optimal transport metrics with information-theoretic measures. Our bound motivates a new algorithm for DG comprising Wasserstein-2 barycenter cost for feature alignment and mutual information or autoencoders for enforcing approximate invertibility. Experiments on several datasets demonstrate superior performance compared to well-known DG algorithms.
翻译:我们重新审视了域通用(DG)问题,这里的假设是由共同代表图组成,然后有一个标签功能。流行的DG方法优化了众所周知的隐蔽域风险的上限。然而,这个约束包含一个术语,由于它双重依赖代表图和未知的隐蔽域最佳标签功能,因此没有优化。我们从一个具有双重依赖性的新上层框中得出这样一个双重依赖性,即对损失函数施加温和的假设,在限制在低维度数据元件时,代表图中要求不可撤销性。衍生利用了将最佳运输指标与信息理论计量联系起来的旧和近期运输不平等。我们的约束激励了由瓦塞斯坦-2 位调合和相互信息成本构成的DG新算法,或用于执行近似不可逆性的自动算法。对几个数据集的实验表明,与众所周知的D算法相比,其性表现优。