epsgo {c060} R Documentation

## Efficient Parameter Selection via Global Optimization

### Description

Finds an optimal solution for the Q.func function.

### Usage

epsgo(Q.func, bounds,  round.n=5, parms.coding="none",
fminlower=0, flag.find.one.min =FALSE,
show=c("none", "final", "all"), N= NULL, maxevals = 500,
pdf.name=NULL,  pdf.width=12,  pdf.height=12, my.mfrow=c(1,1),
verbose=TRUE, seed=123,  ...  )


### Arguments

 Q.func name of the function to be minimized. bounds bounds for parameters round.n number of digits after comma, default: 5 parms.coding parmeters coding: none or log2, default: none. fminlower minimal value for the function Q.func, default is 0. flag.find.one.min do you want to find one min value and stop? Default: FALSE show show plots of DIRECT algorithm: none, final iteration, all iterations. Default: none N define the number of start points, see details. maxevals the maximum number of DIRECT function evaluations, default: 500. pdf.name pdf name pdf.width default: 12 pdf.height default: 12 my.mfrow default: c(1,1) verbose verbose? default: TRUE. seed seed ... additional argument(s)

### Details

if the number of start points (N) is not defined by the user, it will be defined dependent on the dimensionality of the parameter space. N=10D+1, where D is the number of parameters, but for high dimensional parameter space with more than 6 dimensions, the initial set is restricted to 65. However for one-dimensional parameter space the N is set to 21 due to stability reasons.

The idea of EPSGO (Efficient Parameter Selection via Global Optimization): Beginning from an intial Latin hypercube sampling containing N starting points we train an Online GP, look for the point with the maximal expected improvement, sample there and update the Gaussian Process(GP). Thereby it is not so important that GP really correctly models the error surface of the SVM in parameter space, but that it can give a us information about potentially interesting points in parameter space where we should sample next. We continue with sampling points until some convergence criterion is met.

DIRECT is a sampling algorithm which requires no knowledge of the objective function gradient. Instead, the algorithm samples points in the domain, and uses the information it has obtained to decide where to search next. The DIRECT algorithm will globally converge to the maximal value of the objective function. The name DIRECT comes from the shortening of the phrase 'DIviding RECTangles', which describes the way the algorithm moves towards the optimum.

The code source was adopted from MATLAB originals, special thanks to Holger Froehlich.

### Value

 fmin minimal value of Q.func on the interval defined by bounds. xmin corresponding parameters for the minimum iter number of iterations neval number of visited points maxevals the maximum number of DIRECT function evaluations seed seed bounds bounds for parameters Q.func name of the function to be minimized. points.fmin the set of points with the same fmin Xtrain visited points Ytrain the output of Q.func at visited points Xtrain gp.seed seed for Gaussian Process model.list detailed information of the search process

### Author(s)

Natalia Becker natalia.becker at dkfz.de

### References

Froehlich, H. and Zell, A. (2005) "Effcient parameter selection for support vector machines in classification and regression via model-based global optimization" In Proc. Int. Joint Conf. Neural Networks, 1431-1438 .

Sill M., Hielscher T., Becker N. and Zucknick M. (2014), c060: Extended Inference with Lasso and Elastic-Net Regularized Cox and Generalized Linear Models, Journal of Statistical Software, Volume 62(5), pages 1–22. doi:10.18637/jss.v062.i05

### Examples

## Not run:
set.seed(1010)
n=1000;p=100
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)
beta=rnorm(nzc)
fx= x[,seq(nzc)] %*% beta
eps=rnorm(n)*5
y=drop(fx+eps)
px=exp(fx)
px=px/(1+px)
ly=rbinom(n=length(px),prob=px,size=1)
set.seed(1011)

nfolds = 10
set.seed(1234)
foldid <- balancedFolds(class.column.factor=y.classes, cross.outer=nfolds)

# y - binomial
y.classes<-ifelse(y>= median(y),1, 0)
bounds <- t(data.frame(alpha=c(0, 1)))
colnames(bounds)<-c("lower","upper")

fit <- epsgo(Q.func="tune.glmnet.interval",
bounds=bounds,
parms.coding="none",
seed = 1234,
show="none",
fminlower = -100,
x = x, y = y.classes, family = "binomial",
foldid = foldid,
type.min = "lambda.1se",
type.measure = "mse")
summary(fit)

# y - multinomial: low - low 25%, middle - (25,75)-quantiles, high - larger 75%.
y.classes<-ifelse(y <= quantile(y,0.25),1, ifelse(y >= quantile(y,0.75),3, 2))
bounds <- t(data.frame(alpha=c(0, 1)))
colnames(bounds)<-c("lower","upper")

fit <- epsgo(Q.func="tune.glmnet.interval",
bounds=bounds,
parms.coding="none",
seed = 1234,
show="none",
fminlower = -100,
x = x, y = y.classes, family = "multinomial",
foldid = foldid,
type.min = "lambda.1se",
type.measure = "mse")
summary(fit)

##poisson
N=500; p=20
nzc=5
x=matrix(rnorm(N*p),N,p)
beta=rnorm(nzc)
f = x[,seq(nzc)]
mu=exp(f)
y.classes=rpois(N,mu)

nfolds = 10
set.seed(1234)
foldid <- balancedFolds(class.column.factor=y.classes, cross.outer=nfolds)

fit <- epsgo(Q.func="tune.glmnet.interval",
bounds=bounds,
parms.coding="none",
seed = 1234,
show="none",
fminlower = -100,
x = x, y = y.classes, family = "poisson",
foldid = foldid,
type.min = "lambda.1se",
type.measure = "mse")
summary(fit)

#gaussian
set.seed(1234)
x=matrix(rnorm(100*1000,0,1),100,1000)
y <- x[1:100,1:1000]%*%c(rep(2,5),rep(-2,5),rep(.1,990))

foldid <- rep(1:10,each=10)

fit <- epsgo(Q.func="tune.glmnet.interval",
bounds=bounds,
parms.coding="none",
seed = 1234,
show="none",
fminlower = -100,
x = x, y = y, family = "gaussian",
foldid = foldid,
type.min = "lambda.1se",
type.measure = "mse")
summary(fit)

# y - cox in vingette

## End(Not run)


[Package c060 version 0.3-0 Index]