When training a deep neural network for image classification, one can broadly distinguish between two types of latent features of images that will drive the classification. We can divide latent features into (i) "core" or "conditionally invariant" features $X^\text{core}$ whose distribution $X^\text{core}\vert Y$, conditional on the class $Y$, does not change substantially across domains and (ii) "style" features $X^{\text{style}}$ whose distribution $X^{\text{style}} \vert Y$ can change substantially across domains. Examples for style features include position, rotation, image quality or brightness but also more complex ones like hair color, image quality or posture for images of persons. Our goal is to minimize a loss that is robust under changes in the distribution of these style features. In contrast to previous work, we assume that the domain itself is not observed and hence a latent variable. We do assume that we can sometimes observe a typically discrete identifier or "$\mathrm{ID}$ variable". In some applications we know, for example, that two images show the same person, and $\mathrm{ID}$ then refers to the identity of the person. The proposed method requires only a small fraction of images to have $\mathrm{ID}$ information. We group observations if they share the same class and identifier $(Y,\mathrm{ID})=(y,\mathrm{id})$ and penalize the conditional variance of the prediction or the loss if we condition on $(Y,\mathrm{ID})$. Using a causal framework, this conditional variance regularization (CoRe) is shown to protect asymptotically against shifts in the distribution of the style variables. Empirically, we show that the CoRe penalty improves predictive accuracy substantially in settings where domain changes occur in terms of image quality, brightness and color while we also look at more complex changes such as changes in movement and posture.

中文翻译：

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条件方差惩罚和域转移鲁棒性

在训练用于图像分类的深度神经网络时，人们可以大致区分将驱动分类的两种类型的图像潜在特征。我们可以将潜在特征分为（i）“核心”或“条件不变”特征 $X^\text{core}$ 其分布 $X^\text{core}\vert Y$，条件是类 $Y$，跨域不会发生实质性变化，并且（ii）“风格”特征 $X^{\text{style}}$ 的分布 $X^{\text{style}} \vert Y$ 可以跨域发生重大变化。风格特征的示例包括位置、旋转、图像质量或亮度，但也包括更复杂的特征，如头发颜色、图像质量或人物图像的姿势。我们的目标是最小化在这些风格特征分布变化下稳健的损失。与之前的工作相比，我们假设域本身没有被观察到，因此是一个潜在变量。我们确实假设我们有时可以观察到一个典型的离散标识符或“$\mathrm{ID}$ 变量”。例如，在某些应用中，我们知道两张图片显示的是同一个人，而 $\mathrm{ID}$ 则指代此人的身份。所提出的方法只需要一小部分图像就具有 $\mathrm{ID}$ 信息。如果观察共享相同的类和标识符 $(Y,\mathrm{ID})=(y,\mathrm{id})$，我们将观察分组，如果我们以 $(Y ,\mathrm{ID})$。使用因果框架，这种条件方差正则化 (CoRe) 被证明可以渐近地防止样式变量分布的变化。根据经验，