Counterfactual (Non-)identifiability of Learned Structural Causal Models

Recent advances in probabilistic generative modeling have motivated learning Structural Causal Models (SCM) from observational datasets using deep conditional generative models, also known as Deep Structural Causal Models (DSCM). If successful, DSCMs can be utilized for causal estimation tasks, e.g., for answering counterfactual queries. In this work, we warn practitioners about non-identifiability of counterfactual inference from observational data, even in the absence of unobserved confounding and assuming known causal structure. We prove counterfactual identifiability of monotonic generation mechanisms with single dimensional exogenous variables. For general generation mechanisms with multi-dimensional exogenous variables, we provide an impossibility result for counterfactual identifiability, motivating the need for parametric assumptions. As a practical approach, we propose a method for estimating worst-case errors of learned DSCMs' counterfactual predictions. The size of this error can be an essential metric for deciding whether or not DSCMs are a viable approach for counterfactual inference in a specific problem setting. In evaluation, our method confirms negligible counterfactual errors for an identifiable SCM from prior work, and also provides informative error bounds on counterfactual errors for a non-identifiable synthetic SCM

Deep Causal Learning for Robotic Intelligence

This invited review discusses causal learning in the context of robotic intelligence. The paper introduced the psychological findings on causal learning in human cognition, then it introduced the traditional statistical solutions on causal discovery and causal inference. The paper reviewed recent deep causal learning algorithms with a focus on their architectures and the benefits of using deep nets and discussed the gap between deep causal learning and the needs of robotic intelligence

Causal Autoregressive Flows

Peer reviewe

High fidelity image counterfactuals with probabilistic causal models

We present a general causal generative modelling framework for accurate estimation of high fidelity image counterfactuals with deep structural causal models. Estimation of interventional and counterfactual queries for high-dimensional structured variables, such as images, remains a challenging task. We leverage ideas from causal mediation analysis and advances in generative modelling to design new deep causal mechanisms for structured variables in causal models. Our experiments demonstrate that our proposed mechanisms are capable of accurate abduction and estimation of direct, indirect and total effects as measured by axiomatic soundness of counterfactuals

Normalizing Flows for Interventional Density Estimation

Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the distribution of potential outcomes. In this work, we estimate the density of potential outcomes after Interventional Normalizing Flows. Specifically, we combine two normalizing flows, namely (i) a teacher flow for estimating nuisance parameters and (ii) a student flow for a parametric estimation of the density of potential outcomes. We further develop a tractable optimization objective via a one-step bias correction for an efficient and doubly robust estimation of the student flow parameters. As a result our Interventional Normalizing Flows offer a properly normalized density estimator. Across various experiments, we demonstrate that our Interventional Normalizing Flows are expressive and highly effective, and scale well with both sample size and high-dimensional confounding. To the best of our knowledge, our Interventional Normalizing Flows are the first fully-parametric, deep learning method for density estimation of potential outcomes

On the Tractability of Neural Causal Inference

Roth (1996) proved that any form of marginal inference with probabilistic graphical models (e.g. Bayesian Networks) will at least be NP-hard. Introduced and extensively investigated in the past decade, the neural probabilistic circuits known as sum-product network (SPN) offers linear time complexity. On another note, research around neural causal models (NCM) recently gained traction, demanding a tighter integration of causality for machine learning. To this end, we present a theoretical investigation of if, when, how and under what cost tractability occurs for different NCM. We prove that SPN-based causal inference is generally tractable, opposed to standard MLP-based NCM. We further introduce a new tractable NCM-class that is efficient in inference and fully expressive in terms of Pearl's Causal Hierarchy. Our comparative empirical illustration on simulations and standard benchmarks validates our theoretical proofs.Comment: Main paper: 8 pages, References: 2 pages, Appendix: 5 pages. Figures: 5 main, 2 appendi