Algorithm 3.

Causal Direction Determination

1) Input: observations of ${\left\{V_i\right\}}_1^m$, subset VS, causal skeleton UG.

2) Let R = VS.

3) For each variable Vi in R, let Adi be the set of variables adjacent to Vi in UG. Estimate the dependence between P(Adi) and P(Vi|Adi) using equation (7), and denote the estimation as $\widehat{\mathrm{\Delta }}(i)$. Find the variable Vl in R with the minimum $\widehat{\mathrm{\Delta }}$.

4) Orient all edges incident to Vl in U into Vl. (In other words, make Vl a leaf.)

5) Remove Vl from R.

6) Repeat steps 3, 4, and 5 until only one variable is left in R.

7) Output: Graph UG (with edges between variables in VS oriented).