A Computationally Efficient, Exploratory Approach to Brain Connectivity Incorporating False Discovery Rate Control, A Priori Knowledge, and Group Inference
Algorithm 1
The algorithm.
Input: the data , the undirected edges that are assumed to exist in the true undirected graph
according to prior knowledge, the undirected edges () to be tested from the data ,
and the FDR level for making inference about .
Output: an undirected graph , that is, the value of when the algorithm stops, or equivalently, ,
the edges in .
Notations: denotes the multivariate input data. , denote the vertices. , denote the vertex sets.
denotes an undirected edge. denotes vertices adjacent to in graph . denotes the
conditional independence between and given .
(1) Form an undirected graph from .
(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 and calculate the value .
(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 .
A heuristic modification, named the algorithm, at step 14 removes from as well once
