Intervals of Causal Effects for Learning Causal Graphical Models

Structure learning algorithms aim to retrieve the true causal structure from a set of observations. Most times only an equivalence class can be recovered and a unique model cannot be singled out. We hypothesized that casual directions could be inferred from the assessment of the strength of potential causal effects and such assessment can be computed by intervals comparison strategies. We introduce SLICE (Structural Learning with Intervals of Causal Effects), a new algorithm to decide on unresolved relations, which taps on the computation of causal effects and an acceptability index; a strategy for intervals comparison. For validation purposes, synthetic datasets were generated varying the graph size and density with samples drawn from Gaussian and non-Gaussian distributions. Comparison against LiNGAM is made to establish the performance of SLICE over 1440 scenarios using the normalised structural Hamming distance (SHD). The retrieved structures with SLICE showed smaller SHD values in the Gaussian case, improving the structure of the retrieved causal model in terms of correctly found directions. The acceptability index is a good predictor of the true causal effects (R² = 0.62). The proposed strategy represents a new tool for discovering unravelled causal relations in the presence of observational data only.