NetworkMotif {MR.RGM}

Estimating the uncertainty of a specified network

Description

The NetworkMotif function facilitates uncertainty quantification. Specifically, it determines the proportion of posterior samples that contains the given network structure. To use this function, users may use the Gamma_Pst output obtained from the RGM function.

Usage

NetworkMotif(Gamma, Gamma_Pst)

Arguments

Gamma

A matrix of dimension p * p that signifies a specific network structure among the response variables, where p represents the number of response variables. This matrix is the focus of uncertainty quantification.

Gamma_Pst

An array of dimension p * p * n_pst, where n_pst is the number of posterior samples and p denotes the number of response variables. It comprises the posterior samples of the causal network among the response variables. This input might be obtained from the RGM function. Initially, execute the RGM function and save the resulting Gamma_Pst. Subsequently, utilize this stored Gamma_Pst as input for this function.

Value

The NetworkMotif function calculates the uncertainty quantification for the provided network structure. A value close to 1 indicates that the given network structure is frequently observed in the posterior samples, while a value close to 0 suggests that the given network structure is rarely observed in the posterior samples.

References

Ni, Y., Ji, Y., & Müller, P. (2018). Reciprocal graphical models for integrative gene regulatory network analysis. Bayesian Analysis, 13(4), 1095-1110. doi:10.1214/17-BA1087.

Examples

#' # ---------------------------------------------------------

# Example 1:
# Run NetworkMotif to do uncertainty quantification for a given network among the response variable

# Data Generation
set.seed(9154)

# Number of data points
n = 10000

# Number of response variables and number of instrument variables
p = 3
k = 4

# Initialize causal interaction matrix between response variables
A = matrix(sample(c(-0.1, 0.1), p^2, replace = TRUE), p, p)

# Diagonal entries of A matrix will always be 0
diag(A) = 0

# Make the network sparse
A[sample(which(A!=0), length(which(A!=0))/2)] = 0

# Initialize causal interaction matrix between response and instrument variables
B = matrix(0, p, k)

# Create d vector
d = c(2, 1, 1)


# Initialize m
m = 1

# Calculate B matrix based on d vector
for (i in 1:p) {

 # Update ith row of B
 B[i, m:(m + d[i] - 1)] = 1

 # Update m
 m = m + d[i]

}

Sigma = diag(p)

Mult_Mat = solve(diag(p) - A)

Variance = Mult_Mat %*% Sigma %*% t(Mult_Mat)

# Generate instrument data matrix
X = matrix(rnorm(n * k, 0, 1), nrow = n, ncol = k)

# Initialize response data matrix
Y = matrix(0, nrow = n, ncol = p)

# Generate response data matrix based on instrument data matrix
for (i in 1:n) {

    Y[i, ] = MASS::mvrnorm(n = 1, Mult_Mat %*% B %*% X[i, ], Variance)

}


# Apply RGM on individual level data for Threshold Prior
Output = RGM(X = X, Y = Y, d = c(2, 1, 1), prior = "Threshold")

# Store Gamma_Pst
Gamma_Pst = Output$Gamma_Pst

# Define a function to create smaller arrowheads
smaller_arrowheads = function(graph) {
    igraph::E(graph)$arrow.size = 1  # Adjust the arrow size value as needed
    return(graph)
}

# Start with a random subgraph
Gamma = matrix(0, nrow = p, ncol = p)
Gamma[2, 1] = 1

# Plot the subgraph to get an idea about the causal network
plot(smaller_arrowheads(igraph::graph.adjacency(Gamma,
         mode = "directed")), layout = igraph::layout_in_circle,
            main = "Subgraph")


# Do uncertainty quantification for the subgraph
NetworkMotif(Gamma = Gamma, Gamma_Pst = Gamma_Pst)