1,000 samples of 10 variables from a linear-Gaussian model, standardized and rounded to six decimals, seed 4, the columns in an order drawn from the seed. causal-learn's graphs were recorded with causal-learn 0.1.4.8 on the same data.

Method

PC uses the Fisher-z test at alpha 0.05. GES uses the BIC score with the same penalty and parent limit in both packages. A wrong direction includes an edge that is directed in one graph and undirected in the other.

True graph

CPDAG
True edge: sunlight --- temperatureTrue edge: sunlight --> growthTrue edge: rain --> moistureTrue edge: irrigation --> moistureTrue edge: fertilizer --- nitrogenTrue edge: temperature --- pestsTrue edge: temperature --> moistureTrue edge: nitrogen --> growthTrue edge: pests --> yieldTrue edge: moisture --> growthTrue edge: growth --> yieldsunlightrainirrigationfertilizertemperaturenitrogenpestsmoisturegrowthyield

The truth is drawn as its CPDAG, the graph the data can identify. Edges without arrowheads are undirected.

Andrey

PC estimate
Correct: sunlight --- temperatureCorrect: rain --> moistureCorrect: irrigation --> moistureCorrect: fertilizer --- nitrogenCorrect: temperature --- pestsCorrect: temperature --> moistureCorrect: pests --> yieldCorrect: growth --> yieldMissing: the truth has sunlight --> growthWrong direction: nitrogen --- growth here, nitrogen --> growth in the truthWrong direction: growth --> moisture here, moisture --> growth in the truthsunlightrainirrigationfertilizertemperaturenitrogenpestsmoisturegrowthyield
SHD
3
Skeleton F1
0.95
Arrow F1
0.71

8 correct, 1 missing, 0 extra, 2 wrong direction.

Differences
  • Missing: the truth has sunlight --> growth
  • Wrong direction: nitrogen --- growth here, nitrogen --> growth in the truth
  • Wrong direction: growth --> moisture here, moisture --> growth in the truth

causal-learn

PC estimate
Correct: sunlight --- temperatureCorrect: rain --> moistureCorrect: irrigation --> moistureCorrect: fertilizer --- nitrogenCorrect: temperature --- pestsCorrect: temperature --> moistureCorrect: nitrogen --> growthCorrect: moisture --> growthMissing: the truth has sunlight --> growthWrong direction: pests --- yield here, pests --> yield in the truthWrong direction: yield --> growth here, growth --> yield in the truthsunlightrainirrigationfertilizertemperaturenitrogenpestsmoisturegrowthyield
SHD
3
Skeleton F1
0.95
Arrow F1
0.71

8 correct, 1 missing, 0 extra, 2 wrong direction.

Differences
  • Missing: the truth has sunlight --> growth
  • Wrong direction: pests --- yield here, pests --> yield in the truth
  • Wrong direction: yield --> growth here, growth --> yield in the truth

SHD counts missing, extra, and wrong-direction edges; lower SHD is better. Skeleton F1 scores which pairs are joined and arrow F1 scores arrowheads; higher F1 is better.