CMB3S {gfboost}

Column Measure Boosting with SingBoost and Stability Selection (CMB-3S)

Description

Executes CMB and the loss-based Stability Selection.

Usage

CMB3S(
  Dtrain,
  nsing,
  Bsing = 1,
  B = 100,
  alpha = 1,
  singfam = Gaussian(),
  evalfam = Gaussian(),
  sing = FALSE,
  M = 10,
  m_iter = 100,
  kap = 0.1,
  LS = FALSE,
  best = 1,
  wagg,
  gridtype,
  grid,
  Dvalid,
  ncmb,
  robagg = FALSE,
  lower = 0,
  singcoef = FALSE,
  Mfinal = 10,
  ...
)

Arguments

Dtrain

Data matrix. Has to be an n \times (p+1)-dimensional data frame in the format (X,Y). The X-part must not contain an intercept column containing only ones since this column will be added automatically.

nsing

Number of observations (rows) used for the SingBoost submodels.

Bsing

Number of subsamples based on which the SingBoost models are validated. Default is 1. Not to confuse with parameter B for the Stability Selection.

B

Number of subsamples based on which the CMB models are validated. Default is 100. Not to confuse with Bsing for CMB.

alpha

Optional real number in ]0,1]. Defines the fraction of best SingBoost models used in the aggregation step. Default is 1 (use all models).

singfam

A SingBoost family. The SingBoost models are trained based on the corresponding loss function. Default is Gaussian() (squared loss).

evalfam

A SingBoost family. The SingBoost models are validated according to the corresponding loss function. Default is Gaussian() (squared loss).

sing

If sing=FALSE and the singfam family is a standard Boosting family that is contained in the package mboost, the CMB aggregation procedure is executed for the corresponding standard Boosting models.

M

An integer between 2 and m_iter. Indicates that in every M-th iteration, a singular iteration will be performed. Default is 10.

m_iter

Number of SingBoost iterations. Default is 100.

kap

Learning rate (step size). Must be a real number in ]0,1]. Default is 0.1 It is recommended to use a value smaller than 0.5.

LS

If a singfamily object that is already provided by mboost is used, the respective Boosting algorithm will be performed in the singular iterations if Ls is set to TRUE. Default is FALSE.

best

Needed in the case of localized ranking. The parameter K of the localized ranking loss will be computed by best \cdot n (rounded to the next larger integer). Warning: If a parameter K is inserted into the LocRank family, it will be ignored when executing SingBoost.

wagg

Type of row weight aggregation. 'weights1' indicates that the selection frequencies of the (best) SingBoost models are averaged. 'weights2' respects the validation losses for each model and downweights the ones with higher validation losses.

gridtype

Choose between 'pigrid' and 'qgrid'.

grid

The grid for the thresholds (in ]0,1]) or the numbers of final variables (positive integers).

Dvalid

Validation data for selecting the optimal element of the grid and with it the best corresponding model.

ncmb

Number of samples used for CMB. Integer that must be smaller than the number of samples in Dtrain.

robagg

Optional. If setting robagg=TRUE, the best SingBoost models are ignored when executing the aggregation to avoid inlier effects. Only reasonable in combination with lower.

lower

Optional argument. Only reasonable when setting robagg=TRUE. lower is a real number in [0,1[ (a rather small number is recommended) and indicates that the aggregation ignores the SingBoost models with the best performances to avoid possible inlier effects.

singcoef

Default is FALSE. Then the coefficients for the candidate stable models are computed by standard linear regression (provided that the number of columns is smaller than the number of samples in the training set for each grid element). If set to TRUE, the coefficients are computed by SingBoost.

Mfinal

Optional. Necessary if singcoef=TRUE to determine the frequency of singular iterations in the SingBoost models.

...

Optional further arguments

Details

See CMB and CMB.Stabsel.

Value

Final coefficients

The coefficients corresponding to the optimal stable model as a vector.

Stable column measure

Aggregated empirical column measure (i.e., selection frequencies) as a vector.

Selected columns

The column numbers of the variables that form the best stable model as a vector.

Used row measure

Aggregated empirical row measure (i.e., row weights) as a vector.

References

Werner, T., Gradient-Free Gradient Boosting, PhD Thesis, Carl von Ossietzky University Oldenburg, 2020

T. Hothorn, P. Bühlmann, T. Kneib, M. Schmid, and B. Hofner. mboost: Model-Based Boosting, 2017

B. Hofner and T. Hothorn. stabs: Stability Selection with Error Control, 2017.

B. Hofner, L. Boccuto, and M. Göker. Controlling false discoveries in high-dimensional situations: Boosting with stability selection. BMC Bioinformatics, 16(1):144, 2015.

N. Meinshausen and P. Bühlmann. Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(4):417–473, 2010.

Examples

firis<-as.formula(Sepal.Length~.)
Xiris<-model.matrix(firis,iris)
Diris<-data.frame(Xiris[,-1],iris$Sepal.Length)
colnames(Diris)[6]<-"Y"
set.seed(19931023)
ind<-sample(1:150,120,replace=FALSE)
Dtrain<-Diris[ind,]
Dvalid<-Diris[-ind,]
set.seed(19931023)
cmb3s<-CMB3S(Dtrain,nsing=120,Dvalid=Dvalid,ncmb=120,Bsing=1,B=1,alpha=1,singfam=Gaussian()
,evalfam=Gaussian(),sing=FALSE,M=10,m_iter=100,kap=0.1,LS=FALSE,wagg='weights1',
gridtype='pigrid',grid=seq(0.8,0.9,1),robagg=FALSE,lower=0,singcoef=TRUE,Mfinal=10)
cmb3s$Fin
cmb3s$Stab
cmb3s$Sel
glmres4<-glmboost(Sepal.Length~.,iris[ind,])
coef(glmres4)
set.seed(19931023)
cmb3s1<-CMB3S(Dtrain,nsing=80,Dvalid=Dvalid,ncmb=100,Bsing=10,B=100,alpha=0.5,singfam=Gaussian(),
evalfam=Gaussian(),sing=FALSE,M=10,m_iter=100,kap=0.1,LS=FALSE,wagg='weights1',gridtype='pigrid',
grid=seq(0.8,0.9,1),robagg=FALSE,lower=0,singcoef=TRUE,Mfinal=10)
cmb3s1$Fin
cmb3s1$Stab
## This will may take around a minute
set.seed(19931023)
cmb3s2<-CMB3S(Dtrain,nsing=80,Dvalid=Dvalid,ncmb=100,Bsing=10,B=100,alpha=0.5,singfam=Rank(),
evalfam=Rank(),sing=TRUE,M=10,m_iter=100,kap=0.1,LS=TRUE,wagg='weights2',gridtype='pigrid',
grid=seq(0.8,0.9,1),robagg=FALSE,lower=0,singcoef=TRUE,Mfinal=10)
cmb3s2$Fin
cmb3s2$Stab
set.seed(19931023)
cmb3s3<-CMB3S(Dtrain,nsing=80,Dvalid=Dvalid,ncmb=100,Bsing=10,B=100,alpha=0.5,singfam=Huber(),
evalfam=Huber(),sing=FALSE,M=10,m_iter=100,kap=0.1,LS=FALSE,wagg='weights2',gridtype='pigrid',
grid=seq(0.8,0.9,1),robagg=FALSE,lower=0,singcoef=FALSE,Mfinal=10)
cmb3s3$Fin
cmb3s3$Stab