Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference--quantities that are not of direct interest ought to be marginalized out in this process, thus contributing to our overall uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, i.e., for jointly inferring a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient nonlinear additive Gaussian noise models, which we model using Gaussian processes. To capture the space of causal graphs, we use a continuous latent graph representation, allowing our approach to scale to practically relevant problem sizes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, update our beliefs, and repeat. Through simulations, we demonstrate that our approach is more data-efficient than existing methods that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples, while providing well-calibrated uncertainty estimates of the quantities of interest.

We would like to thank the reviewers for their comments and feedback. Janzing et al. [9] write down the same equation, but We will follow the reviewer's The decomposition for conditional SVs follows by replacing "conditioning The decomposition is introduced in Section 3 to assist our illustration of how the different SVs attribute a model's SVs. Unlike conditional (asymmetric) SVs, causal SVs provide the right intuition in the case of common confounding. See also the previous paragraph. SVs appear to fare better than the reviewer suggests.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper deals with the problem of identifiability in the presence of various generated mechanisms for missing data, using a framework introduced by Mohan and others. Some existing results are improved upon, and some nice examples are given (such as identifiability of causal distributions even when conditional distributions are unavailable). Quality Technical quality seems high, the results are very involved but appear to be correct. Results like Theorem 3 are clear and interpretable.

We would like to thank the reviewers for their comments and feedback. Janzing et al. [9] write down the same equation, but We will follow the reviewer's The decomposition for conditional SVs follows by replacing "conditioning The decomposition is introduced in Section 3 to assist our illustration of how the different SVs attribute a model's SVs. Unlike conditional (asymmetric) SVs, causal SVs provide the right intuition in the case of common confounding. See also the previous paragraph. SVs appear to fare better than the reviewer suggests.

Prior-data fitted networks (PFNs) have recently been proposed as a promising way to train tabular foundation models. PFNs are transformers that are pre-trained on synthetic data generated from a prespecified prior distribution and that enable Bayesian inference through in-context learning. In this paper, we introduce CausalFM, a comprehensive framework for training PFN-based foundation models in various causal inference settings. First, we formalize the construction of Bayesian priors for causal inference based on structural causal models (SCMs) in a principled way and derive necessary criteria for the validity of such priors. Building on this, we propose a novel family of prior distributions using causality-inspired Bayesian neural networks that enable CausalFM to perform Bayesian causal inference in various settings, including for back-door, front-door, and instrumental variable adjustment. Finally, we instantiate CausalFM and explicitly train models to perform in-context learning in these settings. We show that CausalFM achieves competitive in-context learning performance even when compared to baselines that are specifically trained for the task at hand. In sum, our framework can be used as a general recipe to train foundation models for various causal inference settings. In contrast to the current state-of-the-art in causal inference, CausalFM offers a novel paradigm with the potential to fundamentally change how practitioners perform causal inference in medicine, economics, and other disciplines.