tetrad_fask
FASK
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1.10.0 |
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Description
From the Tetrad manual: FASK learns a linear model in which all of the variables are skewed.
The idea is as follows. First, FAS-stable is run on the data, producing an undirected graph. We use the BIC score as a conditional independence test with a specified penalty discount c. This yields undirected graph G0 . The reason FAS-stable works for sparse cyclic models where the linear coefficients are all less than 1 is that correlations induced by long cyclic paths are statistically judged as zero, since they are products of multiple coefficients less than 1. Then, each of the X − Y adjacencies in G0 is oriented as a 2-cycle X += Y , or X → Y , or X ← Y . Taking up each adjacency in turn, one tests to see whether the adjacency is a 2-cycle by testing if the difference between corr(X, Y ) and corr(X, Y |X > 0), and corr(X, Y ) and corr(X, Y |Y > 0), are both significantly not zero. If so, the edges X → Y and X ← Y are added to the output graph G1 . If not, the Left-Right orientation is rule is applied: Orient X → Y in G1, if (E(X Y |X > 0)/ E(X 2|X > 0)E(Y 2 |X > 0) − E(X Y |Y > 0)/ E(X 2 |Y > 0)E(Y 2|Y > 0)) > 0; otherwise orient X ← Y . G1 will be a fully oriented graph. For some models, where the true coefficients of a 2-cycle between X and Y are more or less equal in magnitude but opposite in sign, FAS-stable may fail to detect an edge between X and Y when in fact a 2-cycle exists. In this case, we check explicitly whether corr(X, Y |X > 0) and corr(X, Y |Y > 0) differ by more than a set amount of 0.3. If so, the adjacency is added to the graph and oriented using the aforementioned rules.
We include pairwise orientation rule RSkew, Skew, and Tanh from Hyvärinen and Smith[2], so in some configurations FASK can be made to implement an algorithm that has been called in the literature “Pairwise LiNGAM”–this is intentional; we do this for ease of comparison. You’ll get this configuration if you choose one of these pairwise orientation rules, together with the FAS with orientation alpha and two-cycle threshold set to zero and skewness threshold set to 1, for instance.
See Sanchez-Romero et al.[1].
Example JSON
[
{
"id": "fask-fisher-z",
"test": "fisher-z-test",
"score": "sem-bic-score",
"semBicStructurePrior": 1,
"datatype": "continuous",
"timeout": null
}
]