Learning Linear Causal Representations from Interventions under General Nonlinear Mixing
Learning Linear Causal Representations from Interventions under General Nonlinear Mixing
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DOI：
10.48550/arxiv.2306.02235
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Simon Buchholz;Goutham Rajendran;Elan Rosenfeld;Bryon Aragam;B. Scholkopf;Pradeep Ravikumar
中科院分区：
文献类型：
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作者：
Simon Buchholz;Goutham Rajendran;Elan Rosenfeld;Bryon Aragam;B. Scholkopf;Pradeep Ravikumar
我们研究的问题，学习因果表示未知的，潜在的干预在一般情况下，潜在的分布是高斯，但混合函数是完全一般的。我们证明了强大的可识别性结果给定未知的单节点干预，即，而无法接近干预目标。这概括了以前的作品，专注于较弱的类，如线性映射或配对的反事实数据。这也是深度神经网络嵌入的非配对干预的因果可识别性的第一个实例。我们的证明依赖于仔细揭示的高维几何结构存在于数据分布的非线性密度变换后，我们通过分析二次形式的精度矩阵的潜在分布捕获。最后，我们提出了一个对比算法，以确定在实践中的潜变量，并评估其性能的各种任务。
We study the problem of learning causal representations from unknown, latent interventions in a general setting, where the latent distribution is Gaussian but the mixing function is completely general. We prove strong identifiability results given unknown single-node interventions, i.e., without having access to the intervention targets. This generalizes prior works which have focused on weaker classes, such as linear maps or paired counterfactual data. This is also the first instance of causal identifiability from non-paired interventions for deep neural network embeddings. Our proof relies on carefully uncovering the high-dimensional geometric structure present in the data distribution after a non-linear density transformation, which we capture by analyzing quadratic forms of precision matrices of the latent distributions. Finally, we propose a contrastive algorithm to identify the latent variables in practice and evaluate its performance on various tasks.