calibrate_ER: Calibrate ER model to a given density
In systemicrisk: A Toolbox for Systemic Risk
Description
Usage
Arguments
Value
Examples
View source: R/AdjustableModels.R
Description
The model is an Erdos-Renyi model for the existence of links (a
link exists independently of other links with a fixed probability)
and the weight of each existing link follows an exponential
distribution with a fixed rate parameter. This function chooses the
two parameters such that the density of the network (the average
proportion of existing links) is a certain desired value. Diagonal
elements are being set to 0.
Usage
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calibrate_ER(l, a, targetdensity, L_fixed = NA, nsamples_calib = 100,
thin_calib = 100)
Arguments
l
row sums of matrix to be reconstructed
a
column sum of matrix to be reconstructed
targetdensity
desired proportion of reconstructed entries to be positive
L_fixed
Matrix containing known values of L, where NA signifies that
an element is not known. If L_fixed equates to NA (the
default) then no values are assumed to be known.
nsamples_calib
number of matrices to generate during calibration.
thin_calib
amount of thinning to use during calibration
Value
Model that can be used to generate the desired samples using sample_HierarchicalModel.
Examples
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## first generate a true network
n <- 10 # size of network
p <- 0.45
lambda <- 0.1
L <- matrix(nrow=n,rbinom(n*n,prob=p,size=1)*rexp(n*n,rate=lambda))
# then reconstruct with a target density of 0.55
model <- calibrate_ER(l=rowSums(L),a=colSums(L),
targetdensity=0.55,nsamples_calib=10)
Lsamp <- sample_HierarchicalModel(l=rowSums(L),a=colSums(L),model=model,
nsamples=10,thin=1e2)
# check row sums
rowSums(L)
rowSums(Lsamp$L[[10]])
# check calibration
mean(Lsamp$L[[10]]>0)
# now an example with some fixed entries
L_fixed <- L
L_fixed[1:(n/2),] <- NA
# then reconstruct with a target density of 0.9
model <- calibrate_ER(l=rowSums(L),a=colSums(L),L_fixed=L_fixed,
targetdensity=0.9,nsamples_calib=10)
Lsamp <- sample_HierarchicalModel(l=rowSums(L),a=colSums(L),L_fixed=L_fixed,
model=model,nsamples=10,thin=1e2)
mean(Lsamp$L[[10]][-(1:(n/2)),]>0) # known entries
mean(Lsamp$L[[10]][(1:(n/2)),]>0) #reconstructed entries
Example output
p= 0.55
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[1] 96.06403 45.55332 62.87355 26.24573 82.43065 31.58889 38.02474 22.14441
[9] 61.22877 39.84991
[1] 96.06403 45.55332 62.87355 26.24573 82.43065 31.58889 38.02474 22.14441
[9] 61.22877 39.84991
[1] 0.49
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[1] 0.34
[1] 0.9
systemicrisk documentation built on May 2, 2019, 9:26 a.m.
R Package Documentation
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Description Usage Arguments Value Examples
View source: R/AdjustableModels.R
Description
The model is an Erdos-Renyi model for the existence of links (a link exists independently of other links with a fixed probability) and the weight of each existing link follows an exponential distribution with a fixed rate parameter. This function chooses the two parameters such that the density of the network (the average proportion of existing links) is a certain desired value. Diagonal elements are being set to 0.
Usage
1 2 | calibrate_ER(l, a, targetdensity, L_fixed = NA, nsamples_calib = 100,
thin_calib = 100)
|
Arguments
l |
row sums of matrix to be reconstructed |
a |
column sum of matrix to be reconstructed |
targetdensity |
desired proportion of reconstructed entries to be positive |
L_fixed |
Matrix containing known values of L, where NA signifies that
an element is not known. If |
nsamples_calib |
number of matrices to generate during calibration. |
thin_calib |
amount of thinning to use during calibration |
Value
Model that can be used to generate the desired samples using sample_HierarchicalModel.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ## first generate a true network
n <- 10 # size of network
p <- 0.45
lambda <- 0.1
L <- matrix(nrow=n,rbinom(n*n,prob=p,size=1)*rexp(n*n,rate=lambda))
# then reconstruct with a target density of 0.55
model <- calibrate_ER(l=rowSums(L),a=colSums(L),
targetdensity=0.55,nsamples_calib=10)
Lsamp <- sample_HierarchicalModel(l=rowSums(L),a=colSums(L),model=model,
nsamples=10,thin=1e2)
# check row sums
rowSums(L)
rowSums(Lsamp$L[[10]])
# check calibration
mean(Lsamp$L[[10]]>0)
# now an example with some fixed entries
L_fixed <- L
L_fixed[1:(n/2),] <- NA
# then reconstruct with a target density of 0.9
model <- calibrate_ER(l=rowSums(L),a=colSums(L),L_fixed=L_fixed,
targetdensity=0.9,nsamples_calib=10)
Lsamp <- sample_HierarchicalModel(l=rowSums(L),a=colSums(L),L_fixed=L_fixed,
model=model,nsamples=10,thin=1e2)
mean(Lsamp$L[[10]][-(1:(n/2)),]>0) # known entries
mean(Lsamp$L[[10]][(1:(n/2)),]>0) #reconstructed entries
|
Example output
p= 0.55
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[1] 96.06403 45.55332 62.87355 26.24573 82.43065 31.58889 38.02474 22.14441
[9] 61.22877 39.84991
[1] 96.06403 45.55332 62.87355 26.24573 82.43065 31.58889 38.02474 22.14441
[9] 61.22877 39.84991
[1] 0.49
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[1] 0.34
[1] 0.9
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