Unmeasured confounding is a major challenge for identifying causal relationships from non-experimental data. Here, we propose a method that can accommodate unmeasured discrete confounding. Extending recent identifiability results in deep latent variable models, we show theoretically that confounding can be detected and corrected under the assumption that the observed data is a piecewise affine transformation of a latent Gaussian mixture model and that the identity of the mixture components is confounded. We provide a flow-based algorithm to estimate this model and perform deconfounding. Experimental results on synthetic and real-world data provide support for the effectiveness of our approach.

翻译：未测量混杂是识别非实验数据中因果关系的主要挑战。本文提出一种能够处理离散未测量混杂的方法。通过扩展深度潜变量模型中的近期可识别性结果，我们从理论上证明：在观测数据是潜高斯混合模型的分段仿射变换、且混合分量身份存在混杂的假设下，混杂效应可被检测并校正。我们提出一种基于流的算法来估计该模型并执行去混杂操作。在合成数据与真实数据上的实验结果验证了本方法的有效性。