ABSTRACT
To be sure, we already have in hand a clear and plausible method for structure learning with discrete variables: the PC algorithm (Algorithm 8.2) of TETRAD is easily extended to cope with the discrete case. That algorithm implements the VermaPearl constraint-based approach to causal learning by discovering vanishing partial correlations in the data and using them to find direct dependencies (Step 1 of VermaPearl) and v-structure (Step 2). But instead of employing a test for partial correlations between continuous variables, we can substitute a χ2 significance test (see §9.11) comparing P(Y = y|X = x,Z = z) with the expected value if X |= Y |Z, namely P(Y = y|Z = z) — where the P(·) values are actually estimates based on the sample. Thus, we can test directly for conditional independencies with discrete data. This is just what Spirtes et al. in fact did with TETRAD (Spirtes et al., 2000, p. 129).
