Counterfactual image generation is a powerful tool for augmenting training data, de-biasing datasets, and modeling disease. Current approaches rely on external classifiers or regressors to increase the effectiveness of subject-level interventions (e.g., changing the patient's age). For structure-specific interventions (e.g., changing the area of the left lung in a chest radiograph), we show that this is insufficient, and can result in undesirable global effects across the image domain. Previous work used pixel-level label maps as guidance, requiring a user to provide hypothetical segmentations which are tedious and difficult to obtain. We propose Segmentor-guided Counterfactual Fine-Tuning (Seg-CFT), which preserves the simplicity of intervening on scalar-valued, structure-specific variables while producing locally coherent and effective counterfactuals. We demonstrate the capability of generating realistic chest radiographs, and we show promising results for modeling coronary artery disease.

We study a specific type of SCM, called a Dynamic Structural Causal Model (DSCM), whose endogenous variables represent functions of time, which is possibly cyclic and allows for latent confounding. As a motivating use-case, we show that certain systems of Stochastic Differential Equations (SDEs) can be appropriately represented with DSCMs. An immediate consequence of this construction is a graphical Markov property for systems of SDEs. We define a time-splitting operation, allowing us to analyse the concept of local independence (a notion of continuous-time Granger (non-)causality). We also define a subsampling operation, which returns a discrete-time DSCM, and which can be used for mathematical analysis of subsampled time-series. We give suggestions how DSCMs can be used for identification of the causal effect of time-dependent interventions, and how existing constraint-based causal discovery algorithms can be applied to time-series data.

This paper provides a comprehensive review of deep structural causal models (DSCMs), particularly focusing on their ability to answer counterfactual queries using observational data within known causal structures. It delves into the characteristics of DSCMs by analyzing the hypotheses, guarantees, and applications inherent to the underlying deep learning components and structural causal models, fostering a finer understanding of their capabilities and limitations in addressing different counterfactual queries. Furthermore, it highlights the challenges and open questions in the field of deep structural causal modeling. It sets the stages for researchers to identify future work directions and for practitioners to get an overview in order to find out the most appropriate methods for their needs.

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 Model (DSCM). If successful, DSCMs can be utilized for causal estimation tasks, e.g., for answering counterfactual queries (Pawlowski et al. (2020)). 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 Structural Causal Model (SCM) from prior work, and also provides informative error bounds on counterfactual errors for a non-identifiable synthetic SCM.

Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship between Ordinary Differential Equations and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be modelled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria.