Table 1.
Implemention of the new BN structure learning algorithm
| Input: |
| n: number of nodes in the network. |
| D: discretized expression data matrix. |
| BurnIn: number of steps to take before drawing sample networks for evaluation. Default value: 50 times the size of the sampling reservoir. |
| n_iteration: number of iterations. Default value: 80 times the size of the sampling reservoir. |
| Δ_samples: interval of sample networks being collected from the chain after burn-in. Default |
| value: 1000. |
| maxFanIn: maximum number of parents of a node. |
| Output: |
| A set of DAGs after reaching the max iteration step. |
| An average DAG in the form of a matrix. |
| Steps |
| 1. Create a sampling edge reservoir based on plink. |
| 2. Set all elements of the adjacency matrix for the initial DAG to 0. |
| 3. for loop_index = 1: n_iteration do |
| (1) randomly select a element edge(i,j) from the edge sampling reservoir, corresponding to gene pair (i,j). |
| (2) if edge(i,j) exists in the current DAG, delete the edge; else if edge(j,i) exists in the current DAG, reverse edge(j,i) to edge(j,i); else add edge(i,j). We name these operations as "delete", "reverse" and "add", respectively. |
| (3) check whether the newly proposed DAG remains acyclic and satisfy the maxFanIn rules to nodes (i,j). If not, keep the current DAG and give up proposed DAG, go to (1). |
| (4) calculate log value of the marginal likelihood (LL)* of the expression data D of node j and its parents given the current DAG (LL_old) or the proposed DAG (LL_new) and define bf1 = exp(LL_new - LL_old). |
| (5) if the operation is "delete" or "add", bf2 = 1; if the operation is "reverse", calculate bf2 for node i in same way as for node j in (4). |
| (6) calculate the prior probability* of current DAG (prior_old) and propose DAG (prior_new); calculate the Metropolis-Hastings ratio (RHM) of the two DAGs; generate a random number u between 0 to 1, if bf1*bf2*prior_new/prior_old<u*RHM, keep the current DAG and give up proposed DAG, go to (1). |
| (7) when loop_index>BurnIn and (loop_index-BurnIn) is exactly divisible by Δ_samples, record the proposed DAG and its posterior probability. |
| 4. End of loop, calculate the average DAG in the form of a matrix, where the elements are given by the averaged edges of all recorded DAGs weighted by their posterior probabilities. |