Structural Intervention Distance (SID) (package)

Description

The package allows to compute the structural intervention distance (SID) between two graphs. This (pre-)metric evaluates graphs from a causal inference point of view. The package also contains a function for computing the Hamming distance and to generate random DAGs.

Details

Computing the Structural Intervention Distance. The algorithm can be called with structIntervDist.

Author(s)

Jonas Peters <jonas.peters@tuebingen.mpg.de>

References

J. Peters, P. B\"uhlmann: Structural intervention distance (SID) for evaluating causal graphs, Neural Computation 27, pages 771-799, 2015

See Also

randomDAG structIntervDist hammingDist

auxiliary file for SID: computes a path matrix efficiently (can probably be made faster)

Description

auxiliary file for SID: computes a path matrix efficiently (can probably be made faster) This function takes an adjacency matrix G from a DAG and computes a path matrix for which entry(i,j) being one means that there is a directed path from i to j the diagonal will also be one.

Usage

computePathMatrix(G, spars=FALSE)

Arguments

Value

pathMatrix

Author(s)

Jonas Peters <jonas.peters@tuebingen.mpg.de>

See Also

structIntervDist computePathMatrix2

auxiliary file for SID: computes a path matrix efficiently (can probably be made faster)

Description

auxiliary file for SID: computes a path matrix efficiently (can probably be made faster) The only difference to the function computePathMatrix is that this function changes the graph by removing all edges that leave condSet. If condSet is empty, it just returns PathMatrix1.

Usage

computePathMatrix2(G,condSet,PathMatrix1, spars=FALSE)

Arguments

Value

pathMatrix

Author(s)

Jonas Peters <jonas.peters@tuebingen.mpg.de>

See Also

structIntervDist computePathMatrix

Hamming Distance

Description

Computes the Hamming distance between two graph objects.

Usage

hammingDist(G1, G2, allMistakesOne = TRUE)

Arguments

Details

The Hamming distance between two graphs counts the number of edges, in which the graphs do not coincide. allMistakesOne determines whether a reversed edge counts as two or as one mistake. The Hamming distance is symmetric, that is hammingDist(G1,G2) = hammingDist(G2,G1).

Value

The method outputs the computed Hamming distance.

Author(s)

Jonas Peters <jonas.peters@tuebingen.mpg.de>

See Also

structIntervDist

outputs the adjacency matrix of a randomly generated directed acyclic graph (DAG).

Description

After simulating a random topological order first (the order can also be prespecified), the algorithm connects two nodes with the porbability probConnect.

Usage

randomDAG(p, probConnect, causalOrder = sample(p, p, replace = FALSE))

Arguments

Value

p x p adjacency matrix that describes a directed acyclic graph (DAG) with p nodes. The entry (i,j) equals one if and only if there is an edge from i to j.

Author(s)

Jonas Peters <jonas.peters@tuebingen.mpg.de>

See Also

structIntervDist hammingDist

Examples

randomDAG(p = 5, probConnect = 0.6)

Structural Intervention Distance (SID)

Description

computes the structural intervention distance (SID) between two graphs; it evaluates graphs from a causal inference point of view.

Usage

structIntervDist(trueGraph, estGraph, output = FALSE, spars = FALSE)

Arguments

Details

The structural intervention distance (SID) considers each pair (i,j) and checks whether the parents of i in estGraph is a valid adjustment set in trueGraph for the causal effect from i to j. If it is, estimating the causal effect from i to j using parent adjustment in estGraph is a correct procedure, independently of the distribution. If it is not, the pair (i,j) contributes a mistake of one to the overall structural intervention distance.

The SID satisfies the properties of a pre-metric; we have SID(G,G) = 0 and 0 <= SID(G1,G2) <= p(p-1), where p is the number of nodes. The SID is not symmetric: in general, we have SID(G1, G2) != SID(G2,G1). Furthermore, the SID can be zero although the two graphs are not the same.

If estGraph is a completed partially directed acyclic graph (CPDAG), that is it describes a Markov equivalence class, the SID outputs a lower and an upper bound of the SID, that correspond to the best and worst DAG in the equivalence class, respectively.

Value

The main function is structIntervDist. It takes two DAGs (adjacency matrices) of the same dimension as input and provides a list with

Author(s)

Jonas Peters <jonas.peters@tuebingen.mpg.de>

References

J. Peters, P. B\"uhlmann: Structural intervention distance (SID) for evaluating causal graphs, Neural Computation 27, pages 771-799, 2015

See Also

hammingDist randomDAG

Examples

G <- rbind(c(0,1,1,1,1),
           c(0,0,1,1,1),
           c(0,0,0,0,0),
           c(0,0,0,0,0),
           c(0,0,0,0,0))

H1 <- rbind(c(0,1,1,1,1),
            c(0,0,1,1,1),
            c(0,0,0,1,0),
            c(0,0,0,0,0),
            c(0,0,0,0,0))

H2 <- rbind(c(0,0,1,1,1),
            c(1,0,1,1,1),
            c(0,0,0,0,0),
            c(0,0,0,0,0),
            c(0,0,0,0,0))

cat("true DAG G:\n")
show(G)
cat("\n")
cat("==============","\n")
cat("\n")
cat("estimated DAG H1:\n")
show(H1)
sid <- structIntervDist(G,H1)
shd <- hammingDist(G,H1)
cat("SHD between G and H1: ",shd,"\n")
cat("SID between G and H1: ",sid$sid,"\n")
#cat("The matrix of incorrect interventional distributions is: ","\n")
#show(sid$incorrectMat)
cat("\n")
cat("==============","\n")
cat("\n")
cat("estimated DAG H2:\n")
show(H2)
sid <- structIntervDist(G,H2)
shd <- hammingDist(G,H2)
cat("SHD between G and H2: ",shd,"\n")
cat("SID between G and H2: ",sid$sid,"\n")
cat("The matrix of incorrect interventional distributions is: ","\n")
show(sid$incorrectMat)

readline("The SID can also be applied to CPDAGs. Please press enter...")
cat("\n")
cat("==============","\n")
cat("\n")
cat("estimated CPDAG H1c:\n")
H1c <- rbind(c(0,1,1,1,1),c(1,0,1,1,1),c(1,1,0,1,0),c(1,1,1,0,0),c(1,1,0,0,0)) 
show(H1c)
sid <- structIntervDist(G,H1c)
cat("SID between G and H1: \n")
cat("lower bound: ",sid$sidLowerBound," upper bound: ", sid$sidUpperBound, "\n")
cat("\n")