knockoffHMM {SNPknock}

Group knockoffs of hidden Markov models

Description

This function constructs knockoffs of variables distributed as a hidden Markov model.

Usage

knockoffHMM(X, pInit, Q, pEmit, groups = NULL, seed = 123,
  cluster = NULL, display_progress = FALSE)

Arguments

X

an integer matrix of size n-by-p containing the original variables.

pInit

an array of length K, containing the marginal distribution of the states for the first variable.

Q

an array of size (p-1,K,K), containing a list of p-1 transition matrices between the K states of the Markov chain.

pEmit

an array of size (p,M,K), containing the emission probabilities for each of the M possible emission states, from each of the K hidden states and the p variables.

groups

an array of length p, describing the group membership of each variable (default: NULL).

seed

an integer random seed (default: 123).

cluster

a computing cluster object created by makeCluster (default: NULL).

display_progress

whether to show progress bar (default: FALSE).

Details

Each element of the matrix X should be an integer value between 0 and M-1. The transition matrices contained in Q are defined with the same convention as in knockoffDMC. The emission propability matrices contained in pEmit are defined such that P[X_{j}=k|H_{j}=l]=\mathrm{pEmit}[j,k,l], where H_j is the latent variable associated to X_j.

Value

An integer matrix of size n-by-p containing the knockoff variables.

References

Sesia M, Sabatti C, Candès EJ (2019). “Gene hunting with hidden Markov model knockoffs.” Biometrika, 106, 1–18. doi: 10.1093/biomet/asy033. Sesia M, Katsevich E, Bates S, Candès E, Sabatti C (2019). “Multi-resolution localization of causal variants across the genome.” bioRxiv. doi: 10.1101/631390.

See Also

Other knockoffs: knockoffDMC, knockoffGenotypes, knockoffHaplotypes

Examples

# Generate data
p=10; K=5; M=3;
pInit = rep(1/K,K)
Q = array(stats::runif((p-1)*K*K),c(p-1,K,K))
for(j in 1:(p-1)) { Q[j,,] = Q[j,,] / rowSums(Q[j,,]) }
pEmit = array(stats::runif(p*M*K),c(p,M,K))
for(j in 1:p) { pEmit[j,,] = pEmit[j,,] / rowSums(pEmit[j,,]) }
X = sampleHMM(pInit, Q, pEmit, n=20)
# Generate knockoffs
Xk = knockoffHMM(X, pInit, Q, pEmit)
# Generate group-knockoffs for groups of size 3
groups = rep(seq(p), each=3, length.out=p)
Xk = knockoffHMM(X, pInit, Q, pEmit, groups=groups)