Bayesian Active Causal Discovery with Multi-Fidelity Experiments

This paper studies the problem of active causal discovery when the experiments can be done based on multi-fidelity oracles, where higher fidelity experiments are more precise and expensive, while the lower ones are cheaper but less accurate. Comparing with the previous single-fidelity settings, this problem is more practical, since in many real-world applications, people can usually conduct experiments with different costs, precisions and reliabilities. However, this problem also brings more challenges because the model has to make trade-offs to select cheaper oracles which are sufficiently informative to reveal the real causal graph. In this paper, we formally define the task of multi-fidelity active causal discovery, and design a probabilistic model for solving this problem. In specific, we first introduce a mutual-information based acquisition function to determine which variable should be intervened at which fidelity, and then a cascading model is proposed to capture the correlations between different fidelity oracles. Beyond the above basic framework, we also extend it to the multi-target intervention scenario. We find that the theoretical foundations behind the widely used and efficient greedy method do not hold in our problem. To solve this problem, we introduce a new concept called $\epsilon$-submodular, and design a constraint based fidelity model to theoretically validate the greedy method. We conduct extensive experiments to demonstrate the effectiveness of our model. To promote this research direction, we have released our project.