GES Algorithm — Greedy Equivalence Search for Causal Discovery
Greedy Equivalence Search (GES) · Also known as: Greedy Equivalence Search, GES Causal Discovery, Score-Based Greedy Search, Açgözlü Eşdeğerlik Araması
Greedy Equivalence Search (GES) is a score-based algorithm for learning the causal structure of a set of variables from observational data. Introduced by David Maxwell Chickering in 2002, GES operates directly on Markov equivalence classes of directed acyclic graphs (DAGs), represented as completed partially directed acyclic graphs (CPDAGs). Under the assumptions of causal sufficiency and a faithful data-generating process, GES is proven to recover the true equivalence class in the large-sample limit.
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When to use it
Use GES when you have continuous or discrete observational data, assume no hidden confounders (causal sufficiency), and need a provably consistent method for recovering causal structure. It is well-suited to moderately sized variable sets (tens to low hundreds of variables) and outperforms constraint-based methods when sample sizes are small. GES is less appropriate when hidden common causes are suspected (consider FCI instead) or when the variable count is very large, as the search space grows super-exponentially. It also requires a well-specified, decomposable scoring function matched to the data distribution.
Strengths & limitations
- Proven consistency: recovers the true Markov equivalence class in the large-sample limit under causal faithfulness and sufficiency
- Score-based search avoids multiple-testing issues common in constraint-based approaches like PC
- Two-phase structure guarantees the search starts from the empty graph and proceeds monotonically, avoiding many local optima
- Directly outputs a CPDAG, making identifiable and non-identifiable edges explicit
- Assumes causal sufficiency: latent confounders or selection bias can produce incorrect structures
- Computational cost scales poorly with variable count; exact search remains infeasible for large graphs without approximations
- Requires a correctly specified, decomposable score; misspecified scores lead to biased structure recovery
- Faithfulness assumption may be violated in deterministic systems or near-deterministic relationships, causing edge omissions
Frequently asked
How does GES differ from the PC algorithm?
Both target the same CPDAG output, but GES is score-based while PC is constraint-based (conditional independence tests). GES tends to perform better at small sample sizes because it avoids the accumulation of test errors, whereas PC can be faster in sparse high-dimensional graphs. The two approaches are complementary and are often compared as benchmarks in causal discovery studies.
Is GES guaranteed to find the globally optimal graph?
Under causal faithfulness and sufficiency, GES is proven to recover the correct Markov equivalence class asymptotically. In finite samples, greedy search can miss the global optimum if the score landscape has deceptive local plateaus, but empirically GES is competitive with exact methods up to moderate graph sizes.
Can GES handle non-Gaussian or non-linear data?
The classical GES uses a linear-Gaussian BIC score and is not consistent for non-linear or non-Gaussian data without modification. Extensions such as kernel GES (using HSIC-based scores) and nonlinear GES variants address this, but they increase computational cost and may sacrifice some theoretical guarantees. For strongly non-Gaussian linear data, LiNGAM-based methods are often preferred.
Sources
- Chickering, D. M. (2002). Optimal structure identification with greedy search. Journal of Machine Learning Research, 3, 507–554. link ↗
How to cite this page
ScholarGate. (2026, June 2). Greedy Equivalence Search (GES). ScholarGate. https://scholargate.app/en/causal-inference/ges-algorithm
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