aSHD function

Adjusted structural hamming distance (aSHD)

The SHD as implemented in the R package pcalg (Kalisch et al., 2012) and bnlearn(Scutari, 2010), counts how many differences exist between two directed graphs. This distance is 1 if an edge exists in one graph but is missing in the other, or if the direction of an edge is different between the two graphs. The larger this distance is the more different the two graphs are. We adjusted the SHD to reduce the penalty of having the wrong direction of an edge to 0.5. For example, between two graphs V --> T1 <-- T2 and V --> T1 --> T2, the SHD is 1 and the aSHD is 0.5.

aSHD(g1, g2, GV,edge.presence = 1.0, edge.direction = 0.5)

Arguments

• g1: First graph object
• g2: Second graph object
• GV: The number of genetic variants (SNPs/indels/CNV/eQTL) in the input data matrix. For example, if the data has one genetic variant, first column, then GV = 1, if 2, 1st and 2nd column, then GV = 2, and so on.
• edge.presence: The weight for an edge being present.
• edge.direction: The weight for the edge direction.

References

1. Kalisch M, Machler M, Colombo D, Maathuis MH and Buhlmann P (2012). Causal Inference Using Graphical Models with the R Package pcalg. Journal of Statistical Software, 47, 26.

2. Scutari M (2010). Learning Bayesian Networks with the bnlearn R Package. Journal of Statistical Software, 35(3), 1-22.

Author(s)

Md Bahadur Badsha (mbbadshar@gmail.com)

Examples

# True model (V1 --> T1 --> T2 --> T3)
tarmat_s1 <- matrix(0,
                    nrow = 4,
                    ncol = 4)
                    
colnames(tarmat_s1) <- c("V1", "T1", "T2", "T3")

rownames(tarmat_s1) <- colnames(tarmat_s1)

# Create an adjacency matrix for the true graph
tarmat_s1[1, 2] <- 1
tarmat_s1[2, 3] <- 1
tarmat_s1[3, 4] <- 1

# Graph object of the true graph
Truth <- as(tarmat_s1,
            "graphNEL")

# Inferred graph (V1 --> T1 <-- T2 --> T3)
tarmat_s2 <- matrix(0,
                    nrow = 4,
                    ncol = 4)
                    
colnames(tarmat_s2) <-c ("V1", "T1", "T2", "T3")

rownames(tarmat_s2) <- colnames(tarmat_s2)

# Create an adjacency matrix for the inferred graph
tarmat_s2[1, 2] <- 1
tarmat_s2[3, 2] <- 1
tarmat_s2[3, 4] <- 1

# Graph objects for the inferred graph
Inferred <- as(tarmat_s2,
               "graphNEL")

Distance <- aSHD(Truth,
                 Inferred,
                 GV = 1,
                 edge.presence = 1.0,
                 edge.direction = 0.5)