Use What You Know: Causal Foundation Models with Partial Graphs

Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism is the most effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.

Causal questions such as “What happens if we change or intervene on a variable of interest?” are fundamental in science and decision-making. But when we only have observational data, answering these questions reliably requires assumptions, for example about how variables influence one another. Experts often express this knowledge using causal graphs. Recent Causal Foundation Models use large neural networks trained on many simulated causal problems to predict intervention effects automatically, reducing the need to design a specialised method for each new problem. However, current Causal Foundation Models cannot make use of expert causal knowledge when it is available. Our paper addresses this limitation. We show how to equip these models with causal knowledge in the form of graph information, including cases where this knowledge is incomplete. We introduce practical methods for incorporating this information into the model and demonstrate that it leads to more better causal predictions.