Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions - hypothetical "what if?" scenarios that go beyond the observed data and provide insight into a model reasoning. In this work, we introduce the notion of causal interpretability, which formalizes when counterfactual queries can be evaluated from a specific class of models and observational data. We analyze two common model classes - blackbox and concept-based predictors - and show that neither is causally interpretable in general. To address this gap, we develop a framework for building models that are causally interpretable by design. Specifically, we derive a complete graphical criterion that determines whether a given model architecture supports a given counterfactual query. This leads to a fundamental tradeoff between causal interpretability and predictive accuracy, which we characterize by identifying the unique maximal set of features that yields an interpretable model with maximal predictive expressiveness. Experiments corroborate the theoretical findings.

We introduce DeCaFlow, a deconfounding causal generative model. Training once per dataset using just observational data and the underlying causal graph, DeCaFlow enables accurate causal inference on continuous variables under the presence of hidden confounders. Specifically, we extend previous results on causal estimation under hidden confounding to show that a single instance of DeCaFlow provides correct estimates for all causal queries identifiable with do-calculus, leveraging proxy variables to adjust for the causal effects when do-calculus alone is insufficient. Moreover, we show that counterfactual queries are identifiable as long as their interventional counterparts are identifiable, and thus are also correctly estimated by DeCaFlow. Our empirical results on diverse settings--including the Ecoli70 dataset, with 3 independent hidden confounders, tens of observed variables and hundreds of causal queries--show that DeCaFlow outperforms existing approaches, while demonstrating its out-of-the-box applicability to any given causal graph.

Deep neural networks have been criticized as fundamentally statistical systems that fail to capture causal structure and perform causal reasoning. Here we demonstrate that a GPT-style transformer trained for next-token prediction can simultaneously discover instances of linear Gaussian structural causal models (SCMs) and learn to answer counterfactual queries about those SCMs. First, we show that the network generalizes to counterfactual queries about SCMs for which it has seen interventional data but not any examples of counterfactual inference. The network must, thus, have successfully composed discovered causal structures with a learned counterfactual inference algorithm. Second, we decode the implicit "mental" SCM from the network's residual stream activations and manipulate it using gradient descent with predictable effects on the network's output. Our results suggest that statistical prediction may be sufficient to drive the emergence of internal causal models and causal inference capacities in deep neural networks.

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical ``what if?'' scenarios that go beyond the observed data and provide insight into a model reasoning. In this work, we introduce the notion of causal interpretability, which formalizes when counterfactual queries can be evaluated from a specific class of models and observational data. We analyze two common model classes -- blackbox and concept-based predictors -- and show that neither is causally interpretable in general. To address this gap, we develop a framework for building models that are causally interpretable by design. Specifically, we derive a complete graphical criterion that determines whether a given model architecture supports a given counterfactual query. This leads to a fundamental tradeoff between causal interpretability and predictive accuracy, which we characterize by identifying the unique maximal set of features that yields an interpretable model with maximal predictive expressiveness. Experiments corroborate the theoretical findings.

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical ``what if?'' scenarios that go beyond the observed data and provide insight into a model reasoning. In this work, we introduce the notion of causal interpretability, which formalizes when counterfactual queries can be evaluated from a specific class of models and observational data. We analyze two common model classes -- blackbox and concept-based predictors -- and show that neither is causally interpretable in general. To address this gap, we develop a framework for building models that are causally interpretable by design. Specifically, we derive a complete graphical criterion that determines whether a given model architecture supports a given counterfactual query. This leads to a fundamental tradeoff between causal interpretability and predictive accuracy, which we characterize by identifying the unique maximal set of features that yields an interpretable model with maximal predictive expressiveness. Experiments corroborate the theoretical findings.

The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries on all three levels of Pearl's causal hierarchy can be answered: $L_1$ observational, $L_2$ interventional, and $L_3$ counterfactual. An essential aspect of modeling the SCM is to model the dependency of each variable on its causal parents. Traditionally this is done by parametric statistical models, such as linear or logistic regression models. This allows to handle all kinds of data types and fit interpretable models but bears the risk of introducing a bias. More recently neural causal models came up using neural networks (NNs) to model the causal relationships, allowing the estimation of nearly any underlying functional form without bias. However, current neural causal models are generally restricted to continuous variables and do not yield an interpretable form of the causal relationships. Transformation models range from simple statistical regressions to complex networks and can handle continuous, ordinal, and binary data. Here, we propose to use TRAMs to model the functional relationships in SCMs allowing us to bridge the gap between interpretability and flexibility in causal modeling. We call this method TRAM-DAG and assume currently that the underlying directed acyclic graph is known. For the fully observed case, we benchmark TRAM-DAGs against state-of-the-art statistical and NN-based causal models. We show that TRAM-DAGs are interpretable but also achieve equal or superior performance in queries ranging from $L_1$ to $L_3$ in the causal hierarchy. For the continuous case, TRAM-DAGs allow for counterfactual queries for three common causal structures, including unobserved confounding.

This paper broadly considers the use of a learned parametric model. Through (1) toy examples, (2) theoretical analysis of a Dyna-like algorithm, and (3) a large scale study of sample-efficient model-free RL, it arrives at the conclusion that "using an imperfect (e.g., parametric) model to generate fictional experiences from truly observed states… should probably not result in better learning." While the individual pieces described above are all valuable, I am not sure this claim is properly qualified. For example: "More generally, if we use a perfect model to generate experiences only from states that were actually observed, the resulting updates would be indistinguishable from doing experience replay. In a sense, replay is a perfect model, albeit only from the states we have observed." I am not sure this is, as stated, exactly true.

Although deep learning techniques show promising results for many neuroimaging tasks in research settings, they have not yet found widespread use in clinical scenarios. One of the reasons for this problem is that many machine learning models only identify correlations between the input images and the outputs of interest, which can lead to many practical problems, such as encoding of uninformative biases and reduced explainability. Thus, recent research is exploring if integrating a priori causal knowledge into deep learning models is a potential avenue to identify these problems. This work introduces a new causal generative architecture named Masked Causal Flow (MACAW) for neuroimaging applications. Within this context, three main contributions are described. First, a novel approach that integrates complex causal structures into normalizing flows is proposed. Second, counterfactual prediction is performed to identify the changes in effect variables associated with a cause variable. Finally, an explicit Bayesian inference for classification is derived and implemented, providing an inherent uncertainty estimation. The feasibility of the proposed method was first evaluated using synthetic data and then using MRI brain data from more than 23000 participants of the UK biobank study. The evaluation results show that the proposed method can (1) accurately encode causal reasoning and generate counterfactuals highlighting the structural changes in the brain known to be associated with aging, (2) accurately predict a subject's age from a single 2D MRI slice, and (3) generate new samples assuming other values for subject-specific indicators such as age, sex, and body mass index. The code for a toy dataset is available at the following link: https://github.com/vibujithan/macaw-2D.git.