为什么在指数随机图模型(ergm)中引入一个“块”约束参数，大大降低了计算速度？
为什么在指数随机图模型(ergm)中引入一个“块”约束参数，大大降低了计算速度？
提问于 2021-03-31 15:26:39
我试图在加权网络(network_ex)上运行一个值指数随机图模型(ergm)。这个网络显示了四个不同群体中个体之间的相互作用。组之间的交互不能发生，因此需要在模型中包含块对角约束。然而，当我包含这个块对角约束时，计算至少会在蒙特卡罗最大似然估计的一个特定迭代中停留至少24小时(我随后停止了这个过程)。当我删除约束时，计算只需大约30秒。我感到困惑，因为我期望的计算更快与区块对角约束，因为可能变化的边的数目较少。下面是一个类似于我的模型的玩具示例：
library(ergm)
library(ergm.count)
library(tergm)
# define response matrix
mat_ex=matrix(
c(0,1,5,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,5,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,12,1,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,3,6,11,6,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,1,2,6,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,2,0,11,9,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,6,3,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,3,4,8,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,8,1,5,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,6,9,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,3,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,3,0,9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,2,3,0,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,5,3,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,0,2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,7,0,3,3,1,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,6,0,7,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,3,0,1,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,5,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,2,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,1,4,0,0,2,0)
,25,25)
nb=1:25
ID=rep("ID_",25)
names=paste0(ID,nb)
rownames(mat_ex)=names
colnames(mat_ex)=names
# define useful nodes attributes
SeAg=c("F_Adult","F_Adult","M_Adult","M_Adult","M_Sub-Adult","F_Adult","M_Adult","F_Adult","M_Sub-Adult","M_Adult","F_Adult","M_Adult","M_Adult","M_Adult","F_Adult","F_Adult","F_Adult","F_Adult","F_Adult","M_Sub-Adult","M_Adult","M_Adult","M_Adult","F_Adult","M_Adult")
Group=c(1,1,1 ,1,1 ,2, 2, 2 ,2, 2, 2, 2, 3, 3, 3, 3, 3, 4 ,4 ,4, 4, 4, 4,4, 4)
jjj=c(0.9195853,0.5267635,1.0521188,1.4936954,83.8427083,11.3156841,0.6956844,0.2678993,51.5156250,0.7075267,26.5343467,0.7918371,0.3461749,1.5377506,283.7933438,3.2720311,0.9384706,192.6997677,19.0026389,61.6710180,69.0940213,126.9722367,0.5726383,393.5911824,0.7805982)
# define useful edges attributes
mat_iii=matrix(
c(0.0000000000,0.6413537173,1.7611808824,1.1045365579,0.0610428348,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.6413537173,0.0000000000,0.6214644129,1.0141235877,4.9439358178,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,1.7611808824,0.6214644129,0.0000000000,0.2849059121,0.0013686734,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,1.1045365579,1.0141235877,0.2849059121,0.0000000000,0.0374005963
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0610428348,4.9439358178,0.0013686734,0.0374005963
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.4951618629,0.5858325592,3.8541140580,3.7315606330,0.0009005127
,0.3271637800,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.4951618629,0.0000000000,0.2980769040,0.9923034427,1.4379618200
,3.4747962774,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.5858325592,0.2980769040,0.0000000000,0.2162076270
,0.6839987193,0.0000000000,0.1628661860,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,3.8541140580,0.9923034427,0.2162076270
,0.0000000000,1.2295260710,0.0000000000,1.1504634987,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,3.7315606330,1.4379618200
,0.6839987193,1.2295260710,0.0000000000,1.8073008815,0.5011267262,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0009005127
,3.4747962774,0.0000000000,0.0000000000,1.8073008815,0.0000000000,0.0506384403,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.3271637800,0.0000000000,0.1628661860,1.1504634987,0.5011267262,0.0506384403,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,1.6109005375,4.0166662575,0.4233161826,0.1060254672,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,1.6109005375,0.0000000000,0.3408496603,0.4853374582,0.8949786399,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,4.0166662575,0.3408496603,0.0000000000,0.0698993674,0.6698120875,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.4233161826,0.4853374582,0.0698993674,0.0000000000,1.3822143417
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.1060254672,0.8949786399,0.6698120875,1.3822143417
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.3009462716,2.3082969479,0.1018110048,0.0326341498,0.3828057647
,5.5739028034,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.3009462716,0.0000000000,0.2237564859,0.0323276664,3.8922582745
,0.5733125772,0.6159767242,1.1723116376,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,2.3082969479,0.2237564859,0.0000000000,2.3784384336
,0.7850055818,1.5181554486,0.4208603649,1.7763122536,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.1018110048,0.0323276664,2.3784384336
,0.0000000000,0.1936917389,1.7158463101,0.0000000000,0.0289622499,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0326341498,3.8922582745
,0.7850055818,0.1936917389,0.0000000000,0.8168095460,0.9342629045,0.7772395917,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.3828057647
,0.5733125772,1.5181554486,1.7158463101,0.8168095460,0.0000000000,0.0115138397,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,5.5739028034,0.6159767242,0.4208603649,0.0000000000,0.9342629045,0.0115138397,0.0000000000,1.4325614287
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000,0.0000000000
,0.0000000000,0.0000000000,1.1723116376,1.7763122536,0.0289622499,0.7772395917,0.0000000000,1.4325614287
,0.0000000000)
,25,25)
mat_count_ex=matrix(c(0,1,8,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,6,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,4,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,13,2,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,3,13,13,12,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,3,6,9,22,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,2,0,14,11,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,10,3,0,4,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,3,5,10,0,14,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,10,1,6,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,0,4,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,7,12,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,4,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,3,0,13,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,2,4,0,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,5,3,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,3,1,3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,7,1,4,4,3,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,8,0,8,2,0,3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,2,7,0,2,2,3,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,5,5,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,7,0,1,2,0,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,1,2,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,2,6,1,0,5,0),25,25)
# define response network
network_ex=as.network(x = mat_ex,
directed = TRUE,
loops = FALSE,
matrix.type = "adjacency",
ignore.eval=FALSE,
names.eval='weight')
set.vertex.attribute(network_ex, "Sex_Age", as.character(SeAg))
set.vertex.attribute(network_ex, "Group", as.character(Group))
set.vertex.attribute(network_ex, "JJJ", as.numeric(jjj))
set.edge.attribute(network_ex, "III", as.numeric(mat_iii))
set.edge.attribute(network_ex, "Nbobs", as.numeric(mat_count_ex))
# run ergm
ergm_ex <- ergm(network_ex ~
sum
+nonzero
+mutual(form="min",threshold=0)
+nodemix("Sex_Age",levels=c(1,2),form="sum")
+nodeicov("JJJ",form="sum")
+diff("JJJ", pow=1, dir="t-h", sign.action="identity", form ="sum")
+edgecov(mat_iii,"III",form="sum")
+edgecov(mat_count_ex,"Nbobs",form="sum")
,response="weight"
,reference=~Poisson
,constraints = ~blockdiag("Group")
,control = control.ergm(MCMC.interval = 1000
,MCMLE.maxit = 200
,init.method = 'CD'
,MCMC.samplesize = 1000
,MCMC.prop.weights="random"
,MCMC.burnin=100,seed=123456
,parallel=4))我得到的是：
最佳有效建议‘DistRLE’不能考虑提示‘稀疏’。通过CD:迭代1最多60:收敛检验P-值:0E+00开始对比散度估计，对数似然提高了0.9066。迭代2至多60:收敛检验P-值:1.5e-248，对数似然提高了0.4615.迭代3次最多60次:收敛性检验P-值:1.5e-176，对数似然提高了0.6357.迭代4次最多60次:收敛性检验P-值:6.1e-147，对数似然提高了0.4542.迭代5次最多60次:收敛性检验P-值:1.1e-92，对数似然提高了0.2675.迭代6次最多60次:收敛性检验P-值:2.4e-18，对数似然提高了0.04343.迭代7次最多60次:收敛性检验P-值:1.9e-05，对数似然提高了0.01517.迭代8次，最多60次:收敛性检验P-值:4E-04，对数似然提高了0.01191.迭代9次最多60次:收敛性检验P-值:6E-03，对数似然提高了0.009803.迭代10次最多60次:收敛性检验P-值:1.7e-03，对数似然提高了0.01049.迭代11次最多60次:收敛性检验P-值:6.2e-02，对数似然提高了0.006888.迭代12次最多60次:收敛性检验P-值:6E-02，对数似然提高了0.007122.迭代13次最多60次:收敛性检验P-值:2.9e-01，对数似然提高了0.004809.迭代14次，最多60次:收敛性检验P-值:1.5E-02，对数似然提高了0.00833.迭代15次最多60次:收敛性检验P-值:1.6e-01，对数似然提高了0.005631.迭代16次最多60次:收敛性检验P-值:4.3e-01，对数似然提高了0.004001.迭代17次最多60次:收敛性检验P-值:5.8e-01收敛性检测.停下来。对数可能性提高了0.003348.完成的CD。启动蒙特卡罗最大似然估计(MCMLE)：迭代1最多200:步长0.0863421108600662优化。对数可能性提高了2.006.估计方程不在公差范围内。迭代2至多200:优化步长0.0875588561417017。对数可能性提高了2.751.估计方程不在公差范围内。迭代3，最多200次：
它运行得很快，但不再进步。
回答 1
Stack Overflow用户
发布于 2021-03-31 22:46:37
几点建议：
开发版本
- 默认使用自适应MCMC，并自动化了许多其他事情。我建议在
seed=之前(但不包括)删除所有控制参数。(也可能是seed，因为并行处理下的可再现性不是很好。) - 为了更好地了解该函数正在做什么，请传递
verbose=TRUE或verbose=2或更高版本。(更高的数字意味着更多的输出，但它们也可以减慢速度。)为了查看采样器正在做什么，通过parameter. - Unfortunately，控件
- 这个采样器不是很有效，所以实际上您可能需要运行很长时间。(这里有一张票：https://github.com/statnet/ergm.count/issues/5 .)
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https://stackoverflow.com/questions/66890738
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