Likelihood-Free Overcomplete ICA and Applications in Causal Discovery
Likelihood-Free Overcomplete ICA and Applications in Causal Discovery
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发表时间：
2019-09
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通讯作者：
Chenwei Ding;Mingming Gong;Kun Zhang;D. Tao
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作者：
Chenwei Ding;Mingming Gong;Kun Zhang;D. Tao
因果发现在过去几十年中取得了重大进展。特别是，许多最近的因果发现方法利用独立的，非高斯噪声来实现因果模型的可识别性。隐藏的直接共同原因或混杂因素的存在通常会使因果发现更加困难;无论何时，只要它们存在，相应的因果发现算法都可以被视为过完备独立成分分析（OICA）的扩展。然而，现有的OICA算法通常对独立分量的分布做强参数化假设，在真实的数据上可能会违背这一假设，导致次优甚至错误的解。此外，现有的OICA算法依赖于期望最大化（EM）过程，需要计算昂贵的独立分量的后验分布的推断。为了解决这些问题，我们提出了一个似然自由过完备伊卡算法（LFOICA），估计混合矩阵直接通过反向传播没有任何明确的假设上的独立分量的密度函数。由于其计算效率，所提出的方法使得一些因果发现程序更实际可行。为了说明的目的，我们证明了我们的方法在两个因果发现任务的合成和真实的数据的计算效率和功效。
Causal discovery witnessed significant progress over the past decades. In particular, many recent causal discovery methods make use of independent, non-Gaussian noise to achieve identifiability of the causal models. Existence of hidden direct common causes, or confounders, generally makes causal discovery more difficult; whenever they are present, the corresponding causal discovery algorithms can be seen as extensions of overcomplete independent component analysis (OICA). However, existing OICA algorithms usually make strong parametric assumptions on the distribution of independent components, which may be violated on real data, leading to sub-optimal or even wrong solutions. In addition, existing OICA algorithms rely on the Expectation Maximization (EM) procedure that requires computationally expensive inference of the posterior distribution of independent components. To tackle these problems, we present a Likelihood-Free Overcomplete ICA algorithm (LFOICA) that estimates the mixing matrix directly by back-propagation without any explicit assumptions on the density function of independent components. Thanks to its computational efficiency, the proposed method makes a number of causal discovery procedures much more practically feasible. For illustrative purposes, we demonstrate the computational efficiency and efficacy of our method in two causal discovery tasks on both synthetic and real data.