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Constraint-based methods discover causal graphs by testing independences. Score-based methods take a different route. They treat causal discovery as a model selection problem, scoring candidate graphs and searching for the one that best balances fit and complexity.

In this episode, we explore how score-based algorithms learn causal structure, why they hit the same identifiability ceiling as constraint-based methods, and how LLMs can be plugged into the search itself rather than just bolted on at the end.

You’ll learn:

* How score-based methods differ from constraint-based ones: why framing causal discovery as model selection changes both the search procedure and the kinds of errors the algorithm makes.

* Where LLMs can intervene in score-based pipelines: the five integration points, from hard constraints to iterative agentic loops, and which ones are recoverable when the LLM is wrong.

* How to pick the right algorithm and LLM integration strategy: comparing priors, post-hoc orientation, and score augmentation on the Adult Census Income dataset, and what each one is worth in practice.

By the end, you’ll have a clear view of where score-based methods sit relative to constraint-based ones, and a practical map of how to combine statistical search with LLM-derived priors without letting the LLM override the data.

If you’d rather read than listen, the full article (with diagrams, code examples, and implementation details) is available on Substack:

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