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Robust Identifiability in Linear Structural Equation Models of Causal Inference
arXiv - CS - Artificial Intelligence Pub Date : 2020-07-14 , DOI: arxiv-2007.06869 Karthik Abinav Sankararaman, Anand Louis, Navin Goyal
arXiv - CS - Artificial Intelligence Pub Date : 2020-07-14 , DOI: arxiv-2007.06869 Karthik Abinav Sankararaman, Anand Louis, Navin Goyal
In this work, we consider the problem of robust parameter estimation from
observational data in the context of linear structural equation models (LSEMs).
LSEMs are a popular and well-studied class of models for inferring causality in
the natural and social sciences. One of the main problems related to LSEMs is
to recover the model parameters from the observational data. Under various
conditions on LSEMs and the model parameters the prior work provides efficient
algorithms to recover the parameters. However, these results are often about
generic identifiability. In practice, generic identifiability is not sufficient
and we need robust identifiability: small changes in the observational data
should not affect the parameters by a huge amount. Robust identifiability has
received far less attention and remains poorly understood. Sankararaman et al.
(2019) recently provided a set of sufficient conditions on parameters under
which robust identifiability is feasible. However, a limitation of their work
is that their results only apply to a small sub-class of LSEMs, called
``bow-free paths.'' In this work, we significantly extend their work along
multiple dimensions. First, for a large and well-studied class of LSEMs, namely
``bow free'' models, we provide a sufficient condition on model parameters
under which robust identifiability holds, thereby removing the restriction of
paths required by prior work. We then show that this sufficient condition holds
with high probability which implies that for a large set of parameters robust
identifiability holds and that for such parameters, existing algorithms already
achieve robust identifiability. Finally, we validate our results on both
simulated and real-world datasets.
中文翻译:
因果推断的线性结构方程模型的鲁棒可识别性
在这项工作中,我们考虑了线性结构方程模型 (LSEM) 背景下从观测数据中进行稳健参数估计的问题。LSEM 是一类流行且经过充分研究的模型,用于推断自然科学和社会科学中的因果关系。与 LSEM 相关的主要问题之一是从观测数据中恢复模型参数。在 LSEM 和模型参数的各种条件下,先前的工作提供了有效的算法来恢复参数。然而,这些结果通常是关于通用可识别性的。在实践中,通用的可识别性是不够的,我们需要强大的可识别性:观测数据的微小变化不应对参数产生巨大影响。稳健的可识别性受到的关注要少得多,并且仍然知之甚少。桑卡拉曼等人。(2019) 最近提供了一组关于参数的充分条件,在这些条件下,稳健的可识别性是可行的。然而,他们工作的局限性在于他们的结果仅适用于 LSEM 的一个小子类,称为“无弓路径”。在这项工作中,我们在多个维度上显着扩展了他们的工作。首先,对于一大类经过充分研究的 LSEM,即“无弓”模型,我们提供了模型参数的充分条件,在该条件下,稳健的可识别性成立,从而消除了先前工作所需的路径限制。然后,我们证明这种充分条件以高概率成立,这意味着对于大量参数,鲁棒可识别性成立,并且对于这些参数,现有算法已经实现了鲁棒可识别性。最后,
更新日期:2020-07-15
中文翻译:
因果推断的线性结构方程模型的鲁棒可识别性
在这项工作中,我们考虑了线性结构方程模型 (LSEM) 背景下从观测数据中进行稳健参数估计的问题。LSEM 是一类流行且经过充分研究的模型,用于推断自然科学和社会科学中的因果关系。与 LSEM 相关的主要问题之一是从观测数据中恢复模型参数。在 LSEM 和模型参数的各种条件下,先前的工作提供了有效的算法来恢复参数。然而,这些结果通常是关于通用可识别性的。在实践中,通用的可识别性是不够的,我们需要强大的可识别性:观测数据的微小变化不应对参数产生巨大影响。稳健的可识别性受到的关注要少得多,并且仍然知之甚少。桑卡拉曼等人。(2019) 最近提供了一组关于参数的充分条件,在这些条件下,稳健的可识别性是可行的。然而,他们工作的局限性在于他们的结果仅适用于 LSEM 的一个小子类,称为“无弓路径”。在这项工作中,我们在多个维度上显着扩展了他们的工作。首先,对于一大类经过充分研究的 LSEM,即“无弓”模型,我们提供了模型参数的充分条件,在该条件下,稳健的可识别性成立,从而消除了先前工作所需的路径限制。然后,我们证明这种充分条件以高概率成立,这意味着对于大量参数,鲁棒可识别性成立,并且对于这些参数,现有算法已经实现了鲁棒可识别性。最后,