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## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Copyright (C) 2012 - 2022 Reza Mohammadi |
# |
# This file is part of BDgraph package. |
# |
# BDgraph is free software: you can redistribute it and/or modify it under |
# the terms of the GNU General Public License as published by the Free |
# Software Foundation; see <https://cran.r-project.org/web/licenses/GPL-3>.|
# |
# Maintainer: Reza Mohammadi <a.mohammadi@uva.nl> |
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# A divide-and-conquer type greedy hill climb algorithm
# for undirected graphcial models with dicrete data
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# The Hill-Climb algorithm ( function "hill_climb_mpl" ) consists for two part:
# PART 1: Local Marginal Pseudo-likelihood optimization to discovers the Markov
# blanket of each node ( function "local_mb_hc" ).
# PART 2: Neighborhood search algorithm for global Marginal Pseudo-likelihood
# optimization ( function "global_hc" ).
# See "Marginal pseudo-likelihood learning of Markov network structures" by
# Pensar et al. for more details.
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# INPUT: * data (n x p) matrix, as a count dataset with n observations and p variables.
# The outcome space of each variable must be in the form 0, 1, ..., r.
# * alpha: The parameter of the prior distribution
# OUTPUT: * selected_G - adjacency matrix for the selected graph
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
hill_climb_mpl_binary = function( data, freq_data, n, alpha = 0.5, operator = "or" )
{
p = ncol( data )
G = matrix( 0, p, p )
for( i in 1:p )
{
mes = paste( c( " PART 1: Local search for node ", i ), collapse = "" )
cat( mes, "\r" )
utils::flush.console()
mb_i = local_mb_hc_binary( node = i, data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
G[mb_i, i] = 1
}
G_local = matrix( 0, p, p )
if( operator == "or" ) G_local[ ( G + t( G ) ) > 0 ] = 1
if( operator == "and" ) G_local = G * t( G )
if( sum( G_local ) != 0 )
{
selected_G = global_hc_binary( G_local = G_local, data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
}else{
selected_G = G_local
}
return( selected_G )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Local Marginal Pseudo-likelihood optimization to discovers the Markov
# blanket of each node
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
local_mb_hc_binary = function( node, data, freq_data, p, n, alpha = 0.5 )
{
temp = seq_len( p )
mb_potential = temp[ - node ]
l_mb_potential = p - 1
mb_hat = numeric()
log_prob_mb_hat = log_mpl_binary( node, mb_hat, data, freq_data, p, n, alpha = alpha )
cont = TRUE
while( cont == TRUE )
{
cont = FALSE
log_prob_mb_candidates = numeric( l_mb_potential )
for( i in seq_len( l_mb_potential ) )
log_prob_mb_candidates[i] = log_mpl_binary( node = node, mb_node = c( mb_hat, mb_potential[i] ), data = data, freq_data = freq_data, p = p, n = p, alpha = alpha )
log_prob_mb_candidate_top = max( log_prob_mb_candidates )
if( log_prob_mb_candidate_top > log_prob_mb_hat )
{
mb_cand_top_loc = which.max( log_prob_mb_candidates )
mb_hat = c( mb_hat, mb_potential[ mb_cand_top_loc ] )
mb_potential = mb_potential[ - mb_cand_top_loc ]
l_mb_potential = l_mb_potential - 1
log_prob_mb_hat = log_prob_mb_candidate_top
cont = TRUE
}
length_mb_hat = length( mb_hat )
if( ( length_mb_hat > 2 ) & ( cont == TRUE ) )
{
delete = TRUE
while( delete == TRUE )
{
delete = FALSE
log_prob_mb_candidates = numeric( length_mb_hat )
for( i in 1:length_mb_hat )
log_prob_mb_candidates[i] = log_mpl_binary( node = node, mb_node = mb_hat[ -i ], data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
log_prob_mb_candidate_top = max( log_prob_mb_candidates )
if( log_prob_mb_candidate_top > log_prob_mb_hat )
{
mb_cand_top_loc = which.max( log_prob_mb_candidates )
mb_hat = mb_hat[ - mb_cand_top_loc ]
length_mb_hat = length( mb_hat )
log_prob_mb_hat = log_prob_mb_candidate_top
if( length_mb_hat > 2 ) delete = TRUE
}
}
}
}
return( mb_hat )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Neighborhood search algorithm for global Marginal Pseudo-likelihood optimization
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
global_hc_binary = function( G_local, data, freq_data, p, n, alpha = 0.5 )
{
print( "PART 2, running global search algorithm" )
ug = matrix( 0, p, p )
n_edges = sum( G_local ) / 2
temp = which( G_local == 1, arr.ind = T )
edges = temp[temp[, 1] < temp[, 2], ]
curr_scores = numeric( p )
for( i in 1:p )
curr_scores[i] = log_mpl_binary( node = i, which( ug[i, ] == 1 ), data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
edge_change_imp = matrix( 0, n_edges, 2 )
edge_change = matrix( TRUE, n_edges, 2 )
cont = TRUE
while( cont == TRUE )
{
cont = FALSE
edge_change_ind = which( edge_change[, 1] == TRUE )
for( i in 1:length( edge_change_ind ) )
{
edge = edges[edge_change_ind[i], ]
node = edge[1]
mb = which( ug[node, ] == 1 )
if( ug[ edge[1], edge[2] ] == 0 )
{
swoe1 = curr_scores[node]
mb = c( mb, edge[2] )
swe1 = log_mpl_binary( node = node, mb, data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
edge_change_imp[edge_change_ind[i], 1] = swe1 - swoe1;
edge_change[edge_change_ind[i], 1] = FALSE
}else{
swe1 = curr_scores[node]
mb = mb[ mb != edge[2] ]
swoe1 = log_mpl_binary( node = node, mb, data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
edge_change_imp[edge_change_ind[i], 1] = swoe1 - swe1;
edge_change[edge_change_ind[i], 1] = FALSE
}
}
edge_change_ind = which( edge_change[, 2] == 1 )
for( i in 1:length( edge_change_ind ) )
{
edge = edges[edge_change_ind[i], ]
node = edge[2]
mb = which( ug[node, ] == 1 )
if( ug[edge[1], edge[2]] == 0 )
{
swoe2 = curr_scores[node]
mb = c( mb, edge[1] )
swe2 = log_mpl_binary( node = node, mb, data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
edge_change_imp[edge_change_ind[i], 2] = swe2 - swoe2;
edge_change[edge_change_ind[i], 2] = FALSE
}else{
swe2 = curr_scores[node]
mb = mb[mb != edge[1]]
swoe2 = log_mpl_binary( node = node, mb, data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
edge_change_imp[edge_change_ind[i], 2] = swoe2 - swe2;
edge_change[edge_change_ind[i], 2] = FALSE
}
}
imp = apply( edge_change_imp, 1, sum )
max_imp = max( imp )
max_imp_loc = which.max( imp )
if( max_imp > 0 )
{
edge = edges[max_imp_loc, ]
if( ug[edge[1], edge[2]] == 0 )
{
ug[edge[1], edge[2]] = 1
ug[edge[2], edge[1]] = 1
}else{
ug[edge[1], edge[2]] = 0
ug[edge[2], edge[1]] = 0
}
curr_scores[edge[1]] = log_mpl_binary( node = edge[1], which( ug[edge[1], ] == 1 ), data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
curr_scores[edge[2]] = log_mpl_binary( node = edge[2], which( ug[edge[2], ] == 1 ), data = data, freq_data = freq_data, p = p, n = n, alpha = alpha )
edge_change[edges[, 1] == edge[1]|edges[, 1] == edge[2], 1] = TRUE
edge_change[edges[, 2] == edge[1]|edges[, 2] == edge[2], 2] = TRUE
cont = TRUE
}
}
return( ug )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Computing the Marginal pseudo-likelihood for count data
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
log_mpl_binary = function( node, mb_node, data, freq_data, p, n, alpha = 0.5 )
{
mb_node = as.vector( mb_node )
alpha_ijl = alpha
length_freq_data = length( freq_data )
size_node = length( mb_node )
node = node - 1
mb_node = mb_node - 1
log_mpl_node = 0.0
result = .C( "log_mpl_binary_parallel_hc", as.integer(node), as.integer(mb_node), as.integer(size_node),
log_mpl_node = as.double(log_mpl_node), as.integer(data), as.integer(freq_data),
as.integer(length_freq_data), as.double(alpha_ijl),
as.integer(n), PACKAGE = "BDgraph" )
log_mpl_node = result $ log_mpl_node
return( log_mpl_node )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|
