We revisit Domain Generalization (DG) problem, 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 terms 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 the state-of-the-art DG algorithms.
翻译:我们重新审视“通用”(DG)问题,这里的假设是由共同代表图和标签功能构成的。流行的DG方法优化了已知的隐蔽域风险的上限。然而,约束法包含一个术语,由于对代表图的双重依赖以及未知的隐蔽域最佳标签功能,该术语没有优化。我们从一个新的上层框中得出一个具有双重依赖性的条件,即对损失函数施加温和的假设,在限制在低维数据多元的情况下,在代表图上设定可视性要求。衍生法利用了将最佳运输指标与信息理论测量措施相联系的旧和近期运输不平等。我们的约束法激励了由瓦塞斯坦-2巴纳中心(Wasserrstein-2Barnycenter)组成的功能对特征校准成本和相互信息或执行近似可视性应用自动编码的DG算法的新算法。关于几个数据集的实验表明,与最先进的DG算法相比,其表现优。