Evaluating Causal Discovery Algorithms for Path-Specific Fairness and Utility in Healthcare

Causal discovery recovers directed structure from observational data and is increasingly used in clinical settings to support mechanism reasoning and fairness audits of predictive models. Path-specific counterfactual fairness asks whether a protected attribute influences an outcome through illegitimate pathways, but these estimands are defined relative to a supplied causal graph and therefore inherit whatever errors the discovery step introduces. Discovery methods are routinely scored on aggregate structural metrics that weight all edges equally, and no established evaluation asks whether the specific pathway an audit depends on survives discovery---or what the audit reports when that pathway is missing. Here we show that full-graph Graph-of-Thoughts reasoning yields acyclic discovered graphs that are structurally competitive with large language model (LLM) baselines, yet that structural fidelity alone does not guarantee fairness-faithful audits. We introduce GoT-CD, in which the reasoning unit is a complete candidate edge set: multiple graphs are generated in parallel, scored by a deterministic validity function, and merged under a hard union constraint that forbids invented edges, with greedy projection enforcing a DAG before commitment. GoT-CD returns a valid DAG on all five reported benchmarks and achieves the best DAG-valid F1 score among LLM methods on Asia, Alzheimer's, and COVID-Respiratory datasets. On an Alzheimer's benchmark with known unfair path, a post-hoc path-specific audit shows that five of eight discovered graphs recover no path from the sensitive attribute to the outcome and therefore report a null overall effect while mediated effects persist, necessitating downstream path-specific fairness analysis along with structural discovery.

Causal discovery aims to uncover the underlying causal relationships given data generated from a system. The goal, however, is not merely to predict causal edges given data, but also to be able to interpret and explain either observed or hypothesized phenomena, such as a particularly large causal effect. We consider this task of conditional causal discovery and cast it as a Bayesian inference problem, in which we target the posterior over causal graphs and parameters conditional on an event such as a causal-effect constraint. Unfortunately, this poses a computational challenge: existing approaches to Bayesian causal discovery struggle when the event has small posterior mass. To address this, we adapt rare-event estimation techniques to perform inference the joint graph-parameter space. Our method gradually drives a particle population toward the constrained region while maintaining samples that approximate the conditional posterior. Empirical evaluation on synthetic graphs validates the accuracy of our approach at small and large scales, and we show in a case study on the Sachs protein dataset how our method can be used to aid scientific exploration by providing pathway-level summaries.

LLM agents can now run causal discovery algorithms on a dataset and report what comes out. Whether they do more than that, such as noticing where an algorithm went wrong and fixing it with further tests, is hard to tell from current benchmarks. Most of them give the variables meaningful names, and an LLM shown only the names of the Tübingen cause-effect pairs already gets 99% of the directions right. With the names removed, the data are usually clean enough that picking a better algorithm than PC closes most of the gap. We introduce Heuresis, a benchmark of anonymous simulated datasets whose mechanisms range from linear Gaussian to heavy-tailed. For each family of datasets it separates what a better existing algorithm can gain from what only a closer look at the data can gain, and it traces every edge an agent changes. Every family leaves a gap that none of the algorithms, the router and the two causal-discovery foundation models we ran can close, so a score above the best chosen algorithm has to come from using the data. We instantiate the benchmark with an agent harness and three LLMs, GPT-6.1 Sol, Claude Opus 5.5 and Qwen 3.8 Flash. GPT-6.1 Sol surpasses the best chosen algorithm on all six families, by 14% adjacency F1 on the most difficult one, and Claude Opus 5.5 does so by 7.4% there. A third of the true edges the two agents restore on the two hardest families appear in no algorithm's output. The code and data will be publicly released to facilitate future work.