Counterfactual generation lies at the core of various machine learning tasks, including image translation and controllable text generation. This generation process usually requires the identification of the disentangled latent representations, such as content and style, that underlie the observed data. However, it becomes more challenging when faced with a scarcity of paired data and labeling information. Existing disentangled methods crucially rely on oversimplified assumptions, such as assuming independent content and style variables, to identify the latent variables, even though such assumptions may not hold for complex data distributions. For instance, food reviews tend to involve words like tasty, whereas movie reviews commonly contain words such as thrilling for the same positive sentiment. This problem is exacerbated when data are sampled from multiple domains since the dependence between content and style may vary significantly over domains. In this work, we tackle the domain-varying dependence between the content and the style variables inherent in the counterfactual generation task. We provide identification guarantees for such latent-variable models by leveraging the relative sparsity of the influences from different latent variables. Our theoretical insights enable the development of a doMain AdapTive counTerfactual gEneration model, called (MATTE). Our theoretically grounded framework achieves state-of-the-art performance in unsupervised style transfer tasks, where neither paired data nor style labels are utilized, across four large-scale datasets. Code is available at https://github.com/hanqi-qi/Matte.git

翻译：反事实生成是多种机器学习任务的核心，包括图像翻译和可控文本生成。该生成过程通常需要识别观察数据中隐含的解耦潜在表示（如内容和风格）。然而，在配对数据和标签信息稀缺的情况下，这一任务变得更加具有挑战性。现有解耦方法严重依赖于简化假设（如假设内容和风格变量独立）来辨识潜在变量，但此类假设对复杂数据分布可能不成立。例如，美食评论倾向于使用“美味”等词汇，而电影评论中相同积极情感常出现“扣人心弦”等词。当数据从多个域采样时，该问题进一步加剧，因为内容与风格之间的依赖关系可能随域而显著变化。本研究旨在解决反事实生成任务中固有的内容与风格变量之间的域变依赖关系。通过利用不同潜在变量影响的相对稀疏性，我们为这类潜变量模型提供了辨识性保证。基于理论洞见，我们开发了一个名为MATTE的域自适应反事实生成模型。该理论框架在无监督风格迁移任务上取得了最先进的性能（无需使用配对数据或风格标签），并在四个大规模数据集上得到验证。代码已开源至https://github.com/hanqi-qi/Matte.git