A Computationally Efficient, Exploratory Approach to Brain Connectivity Incorporating False Discovery Rate Control, A Priori Knowledge, and Group Inference
Algorithm 3
The gPCfdr algorithm.
Input: the multisubject data , undirected complete graph , complete vertex set and the FDR controlled
level for making inference about .
Output: the recovered undirected graph .
Notations: , denote the vertices. , denote the vertex set. denotes an undirected edge.
denotes vertices adjacent to in graph. denotes the conditional independence between and given .
(1) Form an undirected graph on the vertex set .
(2) Initialize the maximum values associated with the edges in as .
(3) Let depth = 0.
(4) repeat
(5) for each ordered pair of vertices and that and do
(6) for each subset and do
(7) Test hypothesis for each subject and calculate the value at the group level.
(8) if , then
(9) Let .
(10) if every element of has been assigned a valid value by step 9, then
(11) Run the FDR procedure, Algorithm 2, with and as the input.
(12) if the non-existence of certain edges are accepted, then
(13) Remove these edges from .
(14) Update and .
(15) if is removed, then
(16) break the for loop at line 6.
(17) end if
(18) end if
(19) end if
(20) end if
(21) end for
(22) end for
(23) Let .
(24) until for every ordered pair of vertices and that is in .
Note: When a priori knowledge is available, we can also incorporate the prior knowledge into the gPCfdr
algorithm to obtain the algorithm, where the inputs are updated as follows: the multisubject data ,
the undirected edges that are assumed to appear in the true undirected graph according to prior
knowledge, the undirected edges whose existences are to be tested from the data, and the FDR controlled
