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1. Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables

   Bhattacharya, Rohit ; Nabi, Razieh ; Shpitser, Ilya ( October 2022 , Journal of machine learning research)

   Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the identifying functionals they output. In this work, we bridge the gap between identification and estimation of population-level causal effects involving a single treatment and a single outcome. We derive influence function based estimators that exhibit double robustness for the identified effects in a large class of hidden variable DAGs where the treatment satisfies a simple graphical criterion; this class includes models yielding the adjustment and front-door functionals as special cases. We also provide necessary and sufficient conditions under which the statistical model of a hidden variable DAG is nonparametrically saturated and implies no equality constraints on the observed data distribution. Further, we derive an important class of hidden variable DAGs that imply observed data distributions observationally equivalent (up to equality constraints) to fully observed DAGs. In these classes of DAGs, we derive estimators that achieve the semiparametric efficiency bounds for the target of interest where the treatment satisfies our graphical criterion. Finally, we provide a sound and complete identification algorithm that directly yields a weight based estimation strategy for any identifiable effect in hidden variable causal models. 

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2. Causal Inference Despite Limited Global Confounding via Mixture Models

   Gordon, S. ; Mazaheri, B. ; Rabani, Y. ; Schulman, L. ( April 2023 , Proceedings of Machine Learning Research)

   van der Schaar, M. ; Zhang, C. ; Janzing, D. (Ed.)

   A Bayesian Network is a directed acyclic graph (DAG) on a set of n random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite k-mixture of such models is graphically represented by a larger graph which has an additional “hidden” (or “latent”) random variable U, ranging in {1,...,k}, and a directed edge from U to every other vertex. Models of this type are fundamental to causal inference, where U models an unobserved confounding effect of multiple populations, obscuring the causal relationships in the observable DAG. By solving the mixture problem and recovering the joint probability distribution with U, traditionally unidentifiable causal relationships become identifiable. Using a reduction to the more well-studied “product” case on empty graphs, we give the first algorithm to learn mixtures of non-empty DAGs. 

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3. Triad Constraints for Learning Causal Structure of Latent Variables

   Ruichu Cai, Feng Xie ( December 2019 , Advances in neural information processing systems)

   Learning causal structure from observational data has attracted much attention,and it is notoriously challenging to find the underlying structure in the presenceof confounders (hidden direct common causes of two variables). In this paper,by properly leveraging the non-Gaussianity of the data, we propose to estimatethe structure over latent variables with the so-called Triad constraints: we design a form of "pseudo-residual" from three variables, and show that when causal relations are linear and noise terms are non-Gaussian, the causal direction between the latent variables for the three observed variables is identifiable by checking a certain kind of independence relationship. In other words, the Triad constraints help us to locate latent confounders and determine the causal direction between them. This goes far beyond the Tetrad constraints and reveals more information about the underlying structure from non-Gaussian data. Finally, based on the Triad constraints, we develop a two-step algorithm to learn the causal structure corresponding to measurement models. Experimental results on both synthetic and real data demonstrate the effectiveness and reliability of our method. 

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4. Asymmetry Learning for Counterfactually-invariant Classification in OOD Tasks

   Mouli, S Chandra ; Ribeiro, Bruno ( April 2022 , International Conference on Learning Representations)

   Generalizing from observed to new related environments (out-of-distribution) is central to the reliability of classifiers. However, most classifiers fail to predict label from input when the change in environment is due a (stochastic) input transformation not observed in training, as in training we observe , where is a hidden variable. This work argues that when the transformations in train and test are (arbitrary) symmetry transformations induced by a collection of known equivalence relations, the task of finding a robust OOD classifier can be defined as finding the simplest causal model that defines a causal connection between the target labels and the symmetry transformations that are associated with label changes. We then propose a new learning paradigm, asymmetry learning, that identifies which symmetries the classifier must break in order to correctly predict in both train and test. Asymmetry learning performs a causal model search that, under certain identifiability conditions, finds classifiers that perform equally well in-distribution and out-of-distribution. Finally, we show how to learn counterfactually-invariant representations with asymmetry learning in two physics tasks. 

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5. Asymmetry Learning for Counterfactually-invariant Classification in OOD Tasks

   Mouli, S Chandra ; Ribeiro, Bruno ( April 2022 , International Conference on Learning Representations)

   Generalizing from observed to new related environments (out-of-distribution) is central to the reliability of classifiers. However, most classifiers fail to predict label from input when the change in environment is due a (stochastic) input transformation not observed in training, as in training we observe , where is a hidden variable. This work argues that when the transformations in train and test are (arbitrary) symmetry transformations induced by a collection of known equivalence relations, the task of finding a robust OOD classifier can be defined as finding the simplest causal model that defines a causal connection between the target labels and the symmetry transformations that are associated with label changes. We then propose a new learning paradigm, asymmetry learning, that identifies which symmetries the classifier must break in order to correctly predict in both train and test. Asymmetry learning performs a causal model search that, under certain identifiability conditions, finds classifiers that perform equally well in-distribution and out-of-distribution. Finally, we show how to learn counterfactually-invariant representations with asymmetry learning in two physics tasks. 

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