CV.CMB3S {gfboost}

Cross-validated version of CMB-3S

Description

Cross-validates the whole loss-based Stability Selection by aggregating several stable models according to their performance on validation sets. Also computes a cross-validated test loss on a disjoint test set.

Usage

CV.CMB3S(
  D,
  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,
  ncmb,
  CVind,
  targetfam = Gaussian(),
  print = TRUE,
  robagg = FALSE,
  lower = 0,
  singcoef = FALSE,
  Mfinal = 10,
  ...
)

Arguments

D

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).

ncmb

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

CVind

A list where each element contains a vector on length n (number of samples in the data matrix D) which contains the strings 'tr' (training set), 'v' (validation set) and 'te' (test set). This list can be easily generated using the function random_CVind.

targetfam

Target loss. Should be the same family as evalfam. Default is Gaussian() (squared loss).

print

If set to TRUE (default), the number of the currently finished outer cross-validation loop is printed.

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

In CMB3S, a validation set is given based on which the optimal stable model is chosen. The CV.CMB3S function adds an outer cross-validation step such that both the training and the validation data sets (and optionally the test data sets) are chosen randomly by disjointly dividing the initial data set. The aggregated stable models form an ”ultra-stable” model. It is strongly recommended to use this function is a parallelized manner due to huge computation time.

Value

Cross-validated loss

A vector containing the cross-validated test losses.

Ultra-stable column measure

A vector containing the aggregated selection frequencies of the stable models.

References

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