Last data update: 2014.03.03

 R: Parallel sur criterion
sur_optim_parallelR Documentation

Parallel sur criterion

Description

Evaluation of the parallel sur criterion for some candidate points. To be used in optimization routines, like in max_sur_parallel. To avoid numerical instabilities, the new points are evaluated only if they are not too close to an existing observation, or if there is some observation noise. The criterion is the integral of the posterior sur uncertainty.

Usage

sur_optim_parallel(x, integration.points, integration.weights = NULL, 
intpoints.oldmean, intpoints.oldsd, 
precalc.data, model, T, 
new.noise.var = NULL, batchsize, current.sur)

Arguments

x

Input vector of size batchsize*d at which one wants to evaluate the criterion. This argument is NOT a matrix.

integration.points

p*d matrix of points for numerical integration in the X space.

integration.weights

Vector of size p corresponding to the weights of these integration points.

intpoints.oldmean

Vector of size p corresponding to the kriging mean at the integration points before adding the batchsize points x to the design of experiments.

intpoints.oldsd

Vector of size p corresponding to the kriging standard deviation at the integration points before adding the batchsize points x to the design of experiments.

precalc.data

List containing useful data to compute quickly the updated kriging variance. This list can be generated using the precomputeUpdateData function.

model

Object of class km (Kriging model).

T

Target value (scalar).

new.noise.var

Optional scalar value of the noise variance for the new observations.

batchsize

Number of points to sample simultaneously. The sampling criterion will return batchsize points at a time for sampling.

current.sur

Current value of the sur criterion (before adding new observations)

Details

The first argument x has been chosen to be a vector of size batchsize*d (and not a matrix with batchsize rows and d columns) so that an optimizer like genoud can optimize it easily. For example if d=2, batchsize=3 and x=c(0.1,0.2,0.3,0.4,0.5,0.6), we will evaluate the parallel criterion at the three points (0.1,0.2),(0.3,0.4) and (0.5,0.6). The last argument current.sur is used as a default value for the sur criterion when the new points x are too close to existing observations.

Value

Parallel sur value

Author(s)

Clement Chevalier (IMSV, Switzerland, and IRSN, France)

References

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2011), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set ,http://hal.archives-ouvertes.fr/hal-00641108/

Chevalier C., Ginsbourger D. (2012), Corrected Kriging update formulae for batch-sequential data assimilation ,http://arxiv.org/pdf/1203.6452.pdf

See Also

EGIparallel, max_sur_parallel

Examples

#sur_optim_parallel

set.seed(8)
N <- 9 #number of observations
T <- 80 #threshold
testfun <- branin

#a 9 points initial design
design <- data.frame( matrix(runif(2*N),ncol=2) )
response <- testfun(design)

#km object with matern3_2 covariance
#params estimated by ML from the observations
model <- km(formula=~., design = design, 
	response = response,covtype="matern3_2")

###we need to compute some additional arguments:
#integration points, and current kriging means and variances at these points
integcontrol <- list(n.points=50,distrib="sur",init.distrib="MC")
obj <- integration_design(integcontrol=integcontrol,
lower=c(0,0),upper=c(1,1),model=model,T=T)

integration.points <- obj$integration.points
integration.weights <- obj$integration.weights
pred <- predict_nobias_km(object=model,newdata=integration.points,
type="UK",se.compute=TRUE)
intpoints.oldmean <- pred$mean ; intpoints.oldsd<-pred$sd

#another precomputation
precalc.data <- precomputeUpdateData(model,integration.points)

batchsize <- 4
x <- c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8)
#one evaluation of the sur_optim_parallel criterion
#we calculate the expectation of the future "sur" uncertainty 
#when 4 points are added to the doe
#the 4 points are (0.1,0.2) , (0.3,0.4), (0.5,0.6), (0.7,0.8)
sur_optim_parallel(x=x,integration.points=integration.points,
          integration.weights=integration.weights,
          intpoints.oldmean=intpoints.oldmean,intpoints.oldsd=intpoints.oldsd,
          precalc.data=precalc.data,T=T,model=model,
          batchsize=batchsize,current.sur=Inf)


#the function max_sur_parallel will help to find the optimum: 
#ie: the batch of 4 minimizing the expectation of the future uncertainty

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(KrigInv)
Loading required package: DiceKriging
Loading required package: pbivnorm
Loading required package: rgenoud
##  rgenoud (Version 5.7-12.4, Build Date: 2015-07-19)
##  See http://sekhon.berkeley.edu/rgenoud for additional documentation.
##  Please cite software as:
##   Walter Mebane, Jr. and Jasjeet S. Sekhon. 2011.
##   ``Genetic Optimization Using Derivatives: The rgenoud package for R.''
##   Journal of Statistical Software, 42(11): 1-26. 
##

Loading required package: randtoolbox
Loading required package: rngWELL
This is randtoolbox. For overview, type 'help("randtoolbox")'.
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/KrigInv/sur_optim_parallel.Rd_%03d_medium.png", width=480, height=480)
> ### Name: sur_optim_parallel
> ### Title: Parallel sur criterion
> ### Aliases: sur_optim_parallel
> 
> ### ** Examples
> 
> #sur_optim_parallel
> 
> set.seed(8)
> N <- 9 #number of observations
> T <- 80 #threshold
> testfun <- branin
> 
> #a 9 points initial design
> design <- data.frame( matrix(runif(2*N),ncol=2) )
> response <- testfun(design)
> 
> #km object with matern3_2 covariance
> #params estimated by ML from the observations
> model <- km(formula=~., design = design, 
+ 	response = response,covtype="matern3_2")

optimisation start
------------------
* estimation method   : MLE 
* optimisation method : BFGS 
* analytical gradient : used
* trend model : ~X1 + X2
* covariance model : 
  - type :  matern3_2 
  - nugget : NO
  - parameters lower bounds :  1e-10 1e-10 
  - parameters upper bounds :  1.448893 1.853021 
  - best initial criterion value(s) :  -25.38168 

N = 2, M = 5 machine precision = 2.22045e-16
At X0, 0 variables are exactly at the bounds
At iterate     0  f=       25.382  |proj g|=      0.19431
At iterate     1  f =       25.027  |proj g|=       0.13259
At iterate     2  f =       25.014  |proj g|=        1.6725
At iterate     3  f =       25.002  |proj g|=       0.15969
At iterate     4  f =       25.001  |proj g|=       0.17792
At iterate     5  f =       24.999  |proj g|=       0.31318
At iterate     6  f =       24.998  |proj g|=       0.14968
At iterate     7  f =       24.998  |proj g|=       0.03446
At iterate     8  f =       24.998  |proj g|=       0.03458
At iterate     9  f =       24.998  |proj g|=     0.0084816
At iterate    10  f =       24.998  |proj g|=      0.038393
At iterate    11  f =       24.997  |proj g|=        1.3196
At iterate    12  f =       24.997  |proj g|=        1.3327
At iterate    13  f =       24.994  |proj g|=        1.8077
At iterate    14  f =       24.991  |proj g|=        1.8106
At iterate    15  f =       24.975  |proj g|=        1.8136
At iterate    16  f =       24.937  |proj g|=        1.8202
At iterate    17  f =       24.816  |proj g|=        1.8136
At iterate    18  f =       24.652  |proj g|=       0.81261
At iterate    19  f =       24.652  |proj g|=       0.25743
At iterate    20  f =       24.651  |proj g|=     0.0033442
At iterate    21  f =       24.651  |proj g|=    1.4045e-05

iterations 21
function evaluations 30
segments explored during Cauchy searches 22
BFGS updates skipped 0
active bounds at final generalized Cauchy point 1
norm of the final projected gradient 1.40447e-05
final function value 24.6515

F = 24.6515
final  value 24.651471 
converged
> 
> ###we need to compute some additional arguments:
> #integration points, and current kriging means and variances at these points
> integcontrol <- list(n.points=50,distrib="sur",init.distrib="MC")
> obj <- integration_design(integcontrol=integcontrol,
+ lower=c(0,0),upper=c(1,1),model=model,T=T)
> 
> integration.points <- obj$integration.points
> integration.weights <- obj$integration.weights
> pred <- predict_nobias_km(object=model,newdata=integration.points,
+ type="UK",se.compute=TRUE)
> intpoints.oldmean <- pred$mean ; intpoints.oldsd<-pred$sd
> 
> #another precomputation
> precalc.data <- precomputeUpdateData(model,integration.points)
> 
> batchsize <- 4
> x <- c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8)
> #one evaluation of the sur_optim_parallel criterion
> #we calculate the expectation of the future "sur" uncertainty 
> #when 4 points are added to the doe
> #the 4 points are (0.1,0.2) , (0.3,0.4), (0.5,0.6), (0.7,0.8)
> sur_optim_parallel(x=x,integration.points=integration.points,
+           integration.weights=integration.weights,
+           intpoints.oldmean=intpoints.oldmean,intpoints.oldsd=intpoints.oldsd,
+           precalc.data=precalc.data,T=T,model=model,
+           batchsize=batchsize,current.sur=Inf)
[1] 0.01003015
> 
> 
> #the function max_sur_parallel will help to find the optimum: 
> #ie: the batch of 4 minimizing the expectation of the future uncertainty
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>


Created & Maintained by Osamu Ogasawara (osamu.ogasawara@gmail.com) and IMSBIO