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Register a new userCounterexamples to The Blessings of Multiple Causes by Wang and Blei
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Elizabeth Ogburn
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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This note has been updated (April, 2020) to respond to Towards Clarifying the Theory of the Deconfounder by Yixin Wang, David M. Blei (arXiv:2003.04948). This original note, posted in January, 2020, is meant to complement our previous comment on The Blessings of Multiple Causes by Wang and Blei (2019). We provide a more succinct and transparent explanation of the fact that the deconfounder does not control for multi-cause confounding. The argument given in Wang and Blei (2019) makes two mistakes: (1) attempting to infer independence conditional on one variable from independence conditional on a different, unrelated variable, and (2) attempting to infer joint independence from pairwise independence. We give two simple counterexamples to the deconfounder claim.
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This commentary has two goals. We first critically review the deconfounder method and point out its advantages and limitations. We then briefly consider three possible ways to address some of the limitations of the deconfounder method.
(This comment has been updated to respond to Wang and Bleis rejoinder [arXiv:1910.07320].) The premise of the deconfounder method proposed in Blessings of Multiple Causes by Wang and Blei [arXiv:1805.06826], namely that a variable that renders multiple causes conditionally independent also controls for unmeasured multi-cause confounding, is incorrect. This can be seen by noting that no fact about the observed data alone can be informative about ignorability, since ignorability is compatible with any observed data distribution. Methods to control for unmeasured confounding may be valid with additional assumptions in specific settings, but they cannot, in general, provide a checkable approach to causal inference, and they do not, in general, require weaker assumptions than the assumptions that are commonly used for causal inference. While this is outside the scope of this comment, we note that much recent work on applying ideas from latent variable modeling to causal inference problems suffers from similar issues.
Unobserved confounding presents a major threat to causal inference from observational studies. Recently, several authors suggest that this problem may be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that under a linear Gaussian model for the treatments, the causal effect is not identifiable without parametric assumptions on the outcome model. In this paper, we show that the causal effect is indeed identifiable if we assume a general binary choice model for the outcome with a non-probit link. Our identification approach is based on the incongruence between Gaussianity of the treatments and latent confounder, and non-Gaussianity of a latent outcome variable. We further develop a two-step likelihood-based estimation procedure.
We study the identification of direct and indirect causes on time series and provide conditions in the presence of latent variables, which we prove to be necessary and sufficient under some graph constraints. Our theoretical results and estimation algorithms require two conditional independence tests for each observed candidate time series to determine whether or not it is a cause of an observed target time series. We provide experimental results in simulations, as well as real data. Our results show that our method leads to very low false positives and relatively low false negative rates, outperforming the widely used Granger causality.
In the Pioneer 100 (P100) Wellness Project (Price and others, 2017), multiple types of data are collected on a single set of healthy participants at multiple timepoints in order to characterize and optimize wellness. One way to do this is to identify clusters, or subgroups, among the participants, and then to tailor personalized health recommendations to each subgroup. It is tempting to cluster the participants using all of the data types and timepoints, in order to fully exploit the available information. However, clustering the participants based on multiple data views implicitly assumes that a single underlying clustering of the participants is shared across all data views. If this assumption does not hold, then clustering the participants using multiple data views may lead to spurious results. In this paper, we seek to evaluate the assumption that there is some underlying relationship among the clusterings from the different data views, by asking the question: are the clusters within each data view dependent or independent? We develop a new test for answering this question, which we then apply to clinical, proteomic, and metabolomic data, across two distinct timepoints, from the P100 study. We find that while the subgroups of the participants defined with respect to any single data type seem to be dependent across time, the clustering among the participants based on one data type (e.g. proteomic data) appears not to be associated with the clustering based on another data type (e.g. clinical data).
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