Search Algorithms: GES



Introduction

GES is a Bayesian algoirthm (due to Chris Meek) that searches over equivalence classes of statistical models. The GES algorithm was designed to discover causal relationships using observational or mixed observational and experimental data. data.  The algorithm is poitwise consistent under various assumptions including:

There are some differences in assumptions and expected behavior between this algorithm and the PC Algorithm:. When, contrary t oassumptions, there is actually a latent common cause of two measured variables the PC algorithm will sometimes discover that fact; GES will not.

Entering GES parameters

Consider the following example:



When the PC algorithm is chosen from the Search Object combo box, the following window appears:



The parameters that are used by the GES algorithm can be specified in this window. The parameters are as follows:

Execute the search.


Interpreting the output

The GES algorithm returns a partially oriented graph where the nodes represent the variables given as input. In our example, the outcome should be as follows if the sample is representative of the population:



The are basically two types of edges that can appear in GES output:

The absence of an edge between any pair of nodes means they are independent, or that the causal effect of one modelNode in the other is intermediate by other observed variables. Unlike the PC algorithm, no accidental double-directed edges can appear. It does not mean that GES will be immune to the sample variation that caused the unexpected behavior of the PC search. It is a good idea to run both searches and compare the result.

Finally, a triplet of nodes may assume the following pattern:

In other words, in such patterns, A and B are connected by an undirected edge, A and C are connected by an undirected edge, and B and C are not connected by an edge. By the PC search assumptions, this means that B and C cannot both be cause of A. The three possible scenarios are:

In our example, some edges were compelled to be directed: X2 and X3 are causes of X4, and X4 is a cause of X5. However, we cannot tell much about the triplet (X1, X2, X3), but we know that X2 and X3 cannot both be causes of X1.