Description Usage Arguments Details Value Author(s) References See Also Examples
amseLambdaSelection
is a function designed to select the regularization
parameter lambda in graphical models that compromises global clustering structure
and variability of the graph.
1 2 3 4 | amseLambdaSelection(obj, pathIni, y, generator = c("subsampling", "montecarlo"),
pB = 0.7, nite = 10, method = "mb", from = 1, until = NULL,
distF = c("correlation","shortPath"), oneByone = FALSE,
many = 3)
|
obj |
an object of class |
pathIni |
path with best global characteristics (for instance the |
y |
original n\times p data set. |
generator |
type of generator to find the mean squared error: name that uniquely identifies |
pB |
proportion of observations used in subsampling iterations. |
nite |
number of iterations used to estimate the mean square error. |
method |
method used to estimate the networks: name that uniquely identifies |
from |
starting point in lambda sequence. |
until |
last point in lambda sequence. If |
distF |
distance function used to find the dissimilarity matrix from the graph: name that uniquely identifies |
oneByone |
If |
many |
If |
A-MSE algorithm finds λ by minimizing the risk function
R_{AMSE}(λ) = E(∑_{i>j} |δ_{ij}-\hat{δ}_{ij}^{λ}|^2)
where \hat{δ}_{ij}^{λ} is the dissimilarity matrix of the graph
(see graphCorr
). The expected value is approximated by either subsampling or
Monte Carlo and the theoretical δ_{ij} is approximated by the graph in pathIni
.
We recommend using the AGNES algorithm agnesLambdaSelection
to
approximate pathIni
since provides good reference of global network
structure for clustered-based graph structures. Then, A-MSE gives a good trade-off
between graph variability and global network characteristics.
If pathIni
is given by agnesLambdaSelection
and
generator = "subsampling"
, then the lambda selected is always smaller than
the lambda obtained by AGNES
.
The oneByone
approach is suggested to save memory space for very high-dimensional data.
An object of class lambdaSelection
containing the following components:
opt.lambda |
optimal lambda. |
crit.coef |
coefficients for each lambda given the criterion A-MSE. |
criterion |
with value |
Caballe, Adria <a.caballe@sms.ed.ac.uk>, Natalia Bochkina and Claus Mayer.
Caballe, A., N. Bochkina, and C. Mayer (2016). Selection of the Regularization Parameter in Graphical Models using network charactaristics. eprint arXiv:1509.05326, 1-25.
lambdaSelection
for other lambda selection approaches.
1 2 3 4 5 6 7 8 9 10 11 12 13 | # example to use amse function
EX1 <- pcorSimulator(nobs = 70, nclusters = 3, nnodesxcluster = c(40,30,20),
pattern = "powerLaw")
y <- EX1$y
Lambda.SEQ <- seq(.25, 0.70, length.out = 40)
out3 <- huge(y, method = "mb", lambda = Lambda.SEQ)
AG.COEF <- agnesLambdaSelection(out3, distF = "shortPath", way = "direct")
AG.LAMB <- which(AG.COEF$opt.lambda == Lambda.SEQ)
## not run
#AAG.COEF <- amseLambdaSelection(out3, out3$path[[AG.LAMB]], y = y,
# distF = "shortPath", from = AG.LAMB)
#print(AAG.COEF)
|
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