Conditional Independence Test

[zgong001]

The entropy of two different parent sets giving 2 variables are the following. The following is for sprinkler data set.

Suppose X = Fertilizer, Y = MyLawnGreen, W = Sprinkler , Z = NBLawnGreen, W ' = NBLawnWet, Z ' = MyLawnWet

p-value of ( X ind Y | W, Z) = 0.8169111, p-value of ( X ind Y | W ' , Z ' ) = 0.01652227

log Score ( X , Pa (x) = { W, Z } = -52.7119 , log Score ( X , Pa (x) = { W ' , Z ' } = -41.405

entrop (Nwz) = 1.241856 entrop (Nw'z') = 1.204842

[zgong001]

The attachment is the result of Conditional Test Result for sprinkler dataset.

[zgong001]

This attachment is Conditional Independence Test for variable pairs giving one parent.

[zgong001]

Suppose X = Fertilizer, Y = MyLawnGreen, W = Sprinkler , Z = NBLawnGreen, W ' = NBLawnWet, Z ' = MyLawnWet

log Score ( Y , Pa (x) = { W, Z } )= -71.864 , log Score ( X , Pa (x) = { W ' , Z ' } )= -58.1877

entrop (Nxwz) = 1.667553 entrop (Nxw'z') = 1.519601

entrop (Nywz) = 1.841074 entrop (Nyw'z') = 1.678443

[zgong001]

The following is the result of independence Test.
For example:

79 1, 5 | 0, 6 3.834246e-07

The first column is the row number. The 2nd column means children are 1, 5 and parents are 0,6. The 3rd column means the p-value of children 1,5 giving parents 0, 6.

[zgong001]

The following is the entropy of the dataset.

For example:

51 3, 5, 7 1.773572

The first column is the row number. The 2nd column means variables are 3, 5, 7. The 3rd column means the entropy of the variable sets is 1.773572.

[zgong001]

The following is sorted entropy.

[zgong001]

The attachment is Conditional Independence Test result which is sorted based on p-value.

[zgong001]

The attached is the conditional independence test and p-value for sprinkler data sets with 1000 samples.

[zgong001]

The attached is the entropy for sprinkler data sets with 1000 samples.