Description Usage Arguments Details Value Note Author(s) References See Also Examples
The evolutionary Monte Carlo clustering (EMCC) algorithm needs a temperature ladder. This function places the intermediate temperatures between the minimum and the maximum temperature for the ladder.
Below sampDim
refers to the dimension of the sample space,
temperLadderLen
refers to the length of the temperature ladder,
and levelsSaveSampForLen
refers to the length of
levelsSaveSampFor
. Note, this function calls
evolMonteCarloClustering
, so some of the arguments below
have the same name and meaning as the corresponding ones for
evolMonteCarloClustering
. See details below for
explanation on the arguments.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 
nIters 

acceptRatioLimits 

ladderLenMax 

startingVals 

logTarDensFunc 

temperLadder 

temperLimits 

ladderLen 

scheme 

schemeParam 

guideMe 

levelsSaveSampFor 

saveFitness 

verboseLevel 

... 
optional arguments to be passed to 
This function is based on the temperature placement method introduced in section 4.2 of Goswami and Liu (2007).
acceptRatioLimits
This is a range for the estimated acceptance ratios for the random exchange move for the consecutive temperature levels of the final ladder. It is recommended that specified range is between 0.3 and 0.6.
ladderLenMax
It is preferred that one specifies
acceptRatioLimits
for constructing the final temperature
ladder. However, If one has some computational limitations then
one could also specify ladderLenMax
which will limit the
length of the final temperature ladder produced. This also serves
as an upper bound on the number of temperature levels while
placing the intermediate temperatures using the
acceptRatioLimits
.
temperLadder
This is the temperature ladder needed for
the second stage preliminary run. One can either specify a
temperature ladder via temperLadder
or specify
temperLimits
, ladderLen
, scheme
and
schemeParam
. For details on the later set of parameters,
see below. Note, temperLadder
overrides
temperLimits
, ladderLen
, scheme
and
schemeParam
.
temperLimits
temperLimits = c(lowerLimit,
upperLimit)
is a twotuple of positive numbers, where the
lowerLimit
is usually 1 and upperLimit
is a number
in [100, 1000]. If stochastic optimization (via sampling) is the
goal, then lowerLimit
is taken to be in [0, 1]. Often the
upperLimit
is the maximum temperature as suggested by
findMaxTemper
.
ladderLen
, scheme
and schemeParam
These
three parameters are required (along with temperLimits
) if
temperLadder
is not provided. We recommend taking
ladderLen
in [15, 30]. The allowed choices for
scheme
and schemeParam
are:
scheme  schemeParam 
========  ============= 
linear  NA 
log  NA 
geometric  NA 
multpower  NA 
addpower  >= 0 
reciprocal  NA 
exponential  >= 0 
tangent  >= 0 
We recommended using scheme = 'exponential'
and
schemeParam
in [1.5, 2].
guideMe
If guideMe = TRUE
, then the function
suggests different modifications to alter the setting towards a
rerun, in case there are problems with the underlying MCMC run.
levelsSaveSampFor
This is passed to
evolMonteCarlo
for the underlying MCMC run.
This function returns a list with the following components:
finalLadder 
the final temperature ladder found by placing the
intermediate temperatures to be used in 
temperLadder 
the temperature ladder used for the underlying MCMC run. 
acceptRatiosEst 
the estimated acceptance ratios for the random
exchange move for the consecutive temperature levels of

CVSqWeights 
this is the square of the coefficient of variation
of the weights of the importance sampling estimators used to
estimate the acceptance ratios, namely, 
temperLimits 
the sorted 
acceptRatioLimits 
the sorted 
nIters 
the post burnin 
levelsSaveSampFor 
the 
draws 

startingVals 
the 
time 
the time taken by the run. 
The effect of leaving the default value NULL
for some of the
arguments above are as follows:
temperLadder
 valid temperLimits , ladderLen , scheme and
schemeParam

are provided, which are used to construct the temperLadder .


temperLimits
 a valid temperLadder is provided.

levelsSaveSampFor
 temperLadderLen .

Gopi Goswami goswami@stat.harvard.edu
Gopi Goswami and Jun S. Liu (2007). On learning strategies for evolutionary Monte Carlo. Statistics and Computing 17:1:2338.
Gopi Goswami, Jun S. Liu and Wing H. Wong (2007). Evolutionary Monte Carlo Methods for Clustering. Journal of Computational and Graphical Statistics, 16:4:855876.
findMaxTemper
, evolMonteCarloClustering
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 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51  ## The following example is a simple stochastic optimization problem,
## the set up is same as that of findMaxTemper. Here no "heating up"
## is necessary, and hence the maximum temprature is the coldest one,
## namely, 0.5.
##
## However, we do the temperature placement to show how placeTempers
## works, assuming the maximum temperature is 5.
KMeansObj < KMeansFuncGenerator1(97531)
placeTempersObj <
with(KMeansObj,
{
nLevels < 15
sampDim < nrow(yy)
startingVals < sample(c(0, 1),
size = nLevels * sampDim,
replace = TRUE)
startingVals < matrix(startingVals, nrow = nLevels, ncol = sampDim)
placeTempers(nIters = 1000,
acceptRatioLimits = c(0.5, 0.6),
ladderLenMax = 50,
startingVals = startingVals,
logTarDensFunc = logTarDensFunc,
temperLimits = c(0.5, 5),
ladderLen = nLevels,
scheme = 'geometric',
levelsSaveSampFor = seq_len(nLevels),
saveFitness = TRUE,
verboseLevel = 1)
})
print(placeTempersObj)
print(names(placeTempersObj))
with(c(placeTempersObj, KMeansObj),
{
fitnessCol < ncol(draws[ , , 1])
sub < paste('uniform prior on # of clusters: DU[',
priorMinClusters, ', ',
priorMaxClusters, ']', sep = '')
for (ii in rev(seq_along(levelsSaveSampFor))) {
main < paste('EMCC (MAP) clustering (temper = ',
round(temperLadder[levelsSaveSampFor[ii]], 3), ')',
sep = '')
MAPRow < which.min(draws[ , fitnessCol, ii])
clusterPlot(clusterInd = draws[MAPRow, fitnessCol, ii],
data = yy,
main = main,
sub = sub,
knownClusterMeans = knownClusterMeans)
}
})

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