placeTempers {EMCC} | R Documentation |
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.
placeTempers(nIters, acceptRatioLimits, ladderLenMax, startingVals, logTarDensFunc, temperLadder = NULL, temperLimits = NULL, ladderLen = 15, scheme = 'exponential', schemeParam = 1.5, guideMe = TRUE, levelsSaveSampFor = NULL, saveFitness = FALSE, verboseLevel = 0, ...)
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 following arguments.
nIters |
integer > 0. |
acceptRatioLimits |
double vector of two
probabilities. |
ladderLenMax |
integer > 0. |
startingVals |
double matrix of dimension
temperLadderLen x sampDim or vector of
length sampDim , in which case the same starting values are
used for every temperature level. |
logTarDensFunc |
function of two arguments
(draw, ...) that returns the target density evaluated in
the log scale. |
temperLadder |
double vector with all positive
entries, in decreasing order. |
temperLimits |
double vector with two positive
entries. |
ladderLen |
integer > 0. |
scheme |
character . |
schemeParam |
double > 0. |
guideMe |
logical . |
levelsSaveSampFor |
integer vector with positive
entries. |
saveFitness |
logical . |
verboseLevel |
integer , a value >= 2 produces a
lot of output. |
... |
optional arguments to be passed to logTarDensFunc ,
MHPropNewFunc and logMHPropDensFunc . |
This function is based on the temperature placement method introduced in section 4.2 of Goswami and Liu (2007).
acceptRatioLimits
ladderLenMax
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
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 two-tuple 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
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 |
mult-power | NA |
add-power | >= 0 |
reciprocal | NA |
exponential | >= 0 |
tangent | >= 0 |
We recommended using scheme = 'exponential'
and
schemeParam
in [1.5, 2].
guideMe
guideMe = TRUE
, then the function
suggests different modifications to alter the setting towards a
re-run, in case there are problems with the underlying MCMC run.levelsSaveSampFor
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 parallelTempering or
evolMonteCarlo . |
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
temperLadder . |
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, estAcceptRatios . |
temperLimits |
the sorted temperLimits argument. |
acceptRatioLimits |
the sorted acceptRatioLimits argument. |
nIters |
the post burn-in nIters . |
levelsSaveSampFor |
the levelsSaveSampFor argument. |
draws |
array of dimension nIters x
sampDim x levelsSaveSampForLen , if
saveFitness = FALSE . If saveFitness = TRUE , then the
returned array is of dimension nIters x
(sampDim + 1) x levelsSaveSampForLen ;
i.e., each of the levelsSaveSampForLen matrices contain the
fitness values in their last column. |
startingVals |
the startingVals argument. |
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 . |
| a valid temperLadder is provided. |
| temperLadderLen .
|
Gopi Goswami goswami@stat.harvard.edu
Gopi Goswami and Jun S. Liu (2007). On learning strategies for evolutionary Monte Carlo. Statistics and Computing 17:1:23-38.
Gopi Goswami, Jun S. Liu and Wing H. Wong (2007). Evolutionary Monte Carlo Methods for Clustering. Journal of Computational and Graphical Statistics, 16:4:855-876.
findMaxTemper
, evolMonteCarloClustering
## Not run: ## 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 = 5000, 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) } }) ## End(Not run)