Domain generalization (DG) seeks predictors which perform well on unseen test distributions by leveraging data drawn from multiple related training distributions or domains. To achieve this, DG is commonly formulated as an average- or worst-case problem over the set of possible domains. However, predictors that perform well on average lack robustness while predictors that perform well in the worst case tend to be overly-conservative. To address this, we propose a new probabilistic framework for DG where the goal is to learn predictors that perform well with high probability. Our key idea is that distribution shifts seen during training should inform us of probable shifts at test time, which we realize by explicitly relating training and test domains as draws from the same underlying meta-distribution. To achieve probable DG, we propose a new optimization problem called Quantile Risk Minimization (QRM). By minimizing the $\alpha$-quantile of predictor's risk distribution over domains, QRM seeks predictors that perform well with probability $\alpha$. To solve QRM in practice, we propose the Empirical QRM (EQRM) algorithm, and prove: (i) a generalization bound for EQRM; and (ii) that EQRM recovers the causal predictor as $\alpha \to 1$. In our experiments, we introduce a more holistic quantile-focused evaluation protocol for DG, and demonstrate that EQRM outperforms state-of-the-art baselines on CMNIST and several datasets from WILDS and DomainBed.

翻译：为实现这一目标,我们为DG提出了一个新的概率框架,目的是通过利用从多个相关培训分布或域中获取的数据,在秘密测试分布上表现良好。为实现这一目标,DG通常是在一系列可能的域上形成一个平均或最坏的情况问题。然而,平均表现良好的预测数据缺乏稳健性,而在最坏的域中表现良好的预测数据往往过于保守。为了解决这个问题,我们为DG提出了一个新的概率框架,目标是学习表现极有可能的预测数据。我们的关键思想是,培训期间看到的分布变化应告诉我们测试时间可能的变化,我们通过将培训与测试领域明确联系起来,而这是从同一个基本元分布中得出的。然而,为了实现可能的DG,我们提出了一个称为量化风险最小化(QRMM)的新优化问题。通过最大限度地减少预测单位在域内的风险分布,QRM(RM-RM-Q)在总体和 RQ(ERM-RM-RM-Q)中显示一个总质量和最核心的ERMM-RM-RM-RM-QA,并证明我们总和最核心的ERM-RM-RM-RM-RM-RM-RM-Q-RM-Q-RM-RM-RM-A-RAR-RAR-RAR-RAR-R)在总和A-RM-RAR-AR-RF-AR-AR-AR-AR-AR-RM-A-A-A-A-A-A-AD-AD-AD-AD-A-A和AD-AD-AD-AD-AD-A-A-A-RAR-AR-A-A-A-A-A-R-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-RM-RAR-RAR-RAR-RAR-RAR-A-A-A-A-A-R-R-A-A-A-A-A-R-R-R-R-R-RAR-A-A-R-R-R-A-A-A-A-A-A