FGES

Fast Greedy Equivalence Search (FGES) is a scalable variant of the GES algorithm that parallelizes the evaluation of candidate graph modifications and caches computed scores to avoid redundant calculations. Where the original GES recomputes the score of every possible edge addition or deletion at each iteration, FGES precomputes and stores the scores of all local modifications, updating only those affected by the most recent change. This caching strategy reduces the per-iteration complexity from quadratic to near-linear in the number of variables, making FGES feasible for datasets with thousands of variables where GES would be prohibitively slow.

The acceleration comes at a cost. FGES inherits all of GES's structural assumptions — the Faithfulness assumption, causal sufficiency, acyclicity — and adds a new one: that the scoring landscape is smooth enough that local caching does not miss globally optimal modifications. In practice, this assumption is violated near phase transitions and in domains with strong nonlinear interactions, where a small local change can have large non-local score effects. FGES is faster than GES, but it is not necessarily more accurate. Speed and correctness are not the same currency, and the field's emphasis on scalability over reliability reflects a prioritization of what can be computed over what should be believed.