View source: R/catnet.search.R
cnSearchSA | R Documentation |
This function provides a MLE based network search in the space of node orders by Simulated Annealing. For a given sample from an unknown categorical network, it returns a list of catNetwork
objects, with complexity up to some maximal value, that best fit the data.
cnSearchSA(data, perturbations, maxParentSet=0, parentSizes=NULL, maxComplexity=0, nodeCats=NULL, parentsPool=NULL, fixedParents=NULL, edgeProb=NULL, dirProb=NULL, selectMode = "BIC", tempStart=1, tempCoolFact=0.9, tempCheckOrders=10, maxIter=100, orderShuffles=1, stopDiff=0, numThreads=2, priorSearch=NULL, echo=FALSE)
data |
a |
perturbations |
a binary matrix with the dimensions of |
maxParentSet |
an |
parentSizes |
an |
maxComplexity |
an |
nodeCats |
a |
parentsPool |
a |
fixedParents |
a |
edgeProb |
a square |
dirProb |
a square |
selectMode |
a |
tempStart |
a |
tempCoolFact |
a |
tempCheckOrders |
an |
maxIter |
an |
orderShuffles |
a |
stopDiff |
a |
numThreads |
an |
priorSearch |
a |
echo |
a |
The function implements a Simulated Annealing version of the Metropolis algorithm by constructing a Markov chain in the space of node orders. Given a currently selected order, the algorithm tries to improve its likelihood score by exploring its neighborhood. The order score is defined as the likelihood of the selected according to selectMode
network from the set of estimated networks compatible with that order.
The data
can be a matrix of character
categories with rows specifying the node-variables and columns assumed to be independent samples from an unknown network, or
a data.frame
with columns specifying the nodes and rows being the samples.
The number of categories for each node is obtained from the data. It is the user responsibility to make sure the data can be categorized reasonably. If the data is numerical it will be forcibly coerced to integer one, which however may result to NA entries or too many node categories per some nodes, and in either case to the function failure. Use cnDiscretize
to convert numeric data into categorical.
If given, the nodeCats
is used as a list of categories. In that case, nodeCats
should include the node categories presented in the data.
The function returns a list of networks, one for any possible complexity within the specified range. Stochastic optimization, based on the criterion of maximizing the likelihood, is carried on the network with complexity closest to, but not above, maxComplexity
.
If maxComplexity
is not specified, thus the function is called with the default zero value, then maxComplexity
is set to be the complexity of a network with all nodes having the maximum, maxParentSet
, the number of parents.
The selectMode
parameter sets the selection criterion for the network upon which the
maximum likelihood optimization is carried on. "BIC" is the default choice, while any value
different from "AIC" and "BIC" results in the maximum complexity criterion to be used,
the one which selects the network with complexity given by maxComplexity
.
The parameters tempStart
, tempCoolFact
and tempCheckOrders
control the Simulated Annealing schedule.
tempStart
is the starting temperature of the annealing process.
tempCoolFact
is the cooling factor from one temperature step to another.
It is a number between 0 and 1, inclusively;
For example, if tempStart
is the temperature in the first step,
tempStart*tempCoolFact
will be temperature in the second.
tempCheckOrders
is the number of proposals, that is, the candidate orders from the current order neighborhood, to be checked before decreasing the temperature.
If for example maxIter
is 40 and tempCheckOrders
is 4,
then 10 temperature decreasing steps will be eventually performed.
The orderShuffles
parameters controls the extend of the current order neighborhood. A value of zero indicates that random orders should be used as proposals. For positive orderShuffles
's, a candidate order is obtained from the current one by performing orderShuffles
number of times the following operation: a random position is picked up at random (uniformly) and it is exchanged with the position right up next to it. If orderShuffles
is negative, then the operation is: two positions are picked up at random and their values are exchanged.
maxIter
is the maximum length of the Markov chain.
orderShuffles
is a number that controls the extent of the order neighborhoods.
Each new proposed order is obtained from the last accepted one by
orderShuffles
switches of two node indices.
stopDiff
is a stopping criterion. If at a current temperature,
after tempCheckOrders
orders being checked, no likelihood improvement of level at least stopDiff
is found, then the SA stops and the function exists.
Setting this parameter to zero guarantees exhausting all of the maximum allowed
maxIter
order searches.
The function speeds up the Markov Chain by implementing a pre-computing buffer. It runs numThreads
number of parallel threads each of which process a proposed order. If we have more than one acceptance in the batch, the first one is taken as next order selection. The performance boost is more apparent when the Markov chain has a low acceptance rate, in which case the chain can run up to numThreads
-times faster.
priorSearch
is a result from previous search. This parameters allows a new search to be initiated
from the best order found so far. Thus a chain of searches can be constructed with varying parameters
providing greater adaptability and user control.
See the vignettes for more details on the algorithm.
A catNetworkEvaluate
object.
N. Balov, P. Salzman
cnSearchOrder
cnet <- cnRandomCatnet(numnodes=6, maxParents=2, numCategories=2) psamples <- cnSamples(object=cnet, numsamples=100) nets <- cnSearchSA(data=psamples, perturbations=NULL, maxParentSet=1, maxComplexity=16) cc <- cnComplexity(object=cnet) cnFind(object=nets, complexity=cc)
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