It can be argued that finding an interpretable low-dimensional representation of a potentially high-dimensional phenomenon is central to the scientific enterprise. Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. This work proposes mechanism sparsity regularization as a new principle to achieve nonlinear ICA when latent factors depend sparsely on observed auxiliary variables and/or past latent factors. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse and if some graphical criterion is satisfied by the data generating process. As a special case, our framework shows how one can leverage unknown-target interventions on the latent factors to disentangle them, thus drawing further connections between ICA and causality. We validate our theoretical results with toy experiments.
翻译:可以认为,找到一种可解释的、低维度的潜在高维现象是科学企业的核心。独立组成部分分析(ICA)是指将这一目标正式化并提供实际应用估计程序的一系列方法。这项工作建议将机制宽度规范化作为实现非线性ICA的新原则,因为潜伏因素很少依赖于观测到的辅助变量和/或过去的潜伏因素。我们表明,如果将稀疏的潜在机制规范化,如果数据生成过程满足了某些图形标准,潜伏变量可以恢复到一种变异状态。作为一个特例,我们的框架表明,人们如何利用未知目标的干预手段来消除这些潜在因素,从而在ICA和因果关系之间进一步建立联系。我们用微量实验来验证我们的理论结果。