BOSO: BOSO and associates functions
In BOSO: Bilevel Optimization Selector Operator

Description Usage Arguments Details Value Author(s) Examples

View source: R/BOSO.R

Fit a ridge linear regression by a feature selection model conducted by BOSO MILP. The package 'cplexAPI' is necessary to run it.

BOSO(
  x,
  y,
  xval,
  yval,
  IC = "eBIC",
  IC.blocks = NULL,
  nlambda = 100,
  nlambda.blocks = 10,
  lambda.min.ratio = ifelse(nrow(x) < ncol(x), 0.01, 1e-04),
  lambda = NULL,
  intercept = TRUE,
  standardize = TRUE,
  dfmax = NULL,
  maxVarsBlock = 10,
  costErrorVal = 1,
  costErrorTrain = 0,
  costVars = 0,
  Threads = 0,
  timeLimit = 1e+75,
  verbose = F,
  seed = NULL,
  warmstart = F,
  TH_IC = 0.001,
  indexSelected = NULL
)

`x`	Input matrix, of dimension 'n' x 'p'. This is the data from the training partition. Its recommended to be class "matrix".
`y`	Response variable for the training dataset. A matrix of one column or a vector, with 'n' elements.
`xval`	Input matrix, of dimension 'n' x 'p'. This is the data from the validation partition. Its recommended to be class "matrix".
`yval`	Response variable for the validation dataset. A matrix of one column or a vector, with 'n' elements.
`IC`	information criterion to be used. Default is 'eBIC'.
`IC.blocks`	information criterion to be used in the block strategy. Default is the same as IC, but eBIC uses BIC for the block strategy.
`nlambda`	The number of lambda values. Default is 100.
`nlambda.blocks`	The number of lambda values in the block strategy part. Default is 10.
`lambda.min.ratio`	Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value.
`lambda`	A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this. WARNING: use with care.
`intercept`	Boolean variable to indicate if intercept should be added or not. Default is false.
`standardize`	Boolean variable to indicate if data should be scaled according to mean(x) mean(y) and sd(x) or not. Default is false.
`dfmax`	Maximum number of variables to be included in the problem. The intercept is not included in this number. Default is min(p,n).
`maxVarsBlock`	maximum number of variables in the block strategy.
`costErrorVal`	Cost of error of the validation set in the objective function. Default is 1. WARNING: use with care, changing this value changes the formulation presented in the main article.
`costErrorTrain`	Cost of error of the training set in the objective function. Default is 0. WARNING: use with care, changing this value changes the formulation presented in the main article.
`costVars`	Cost of new variables in the objective function. Default is 0. WARNING: use with care, changing this value changes the formulation presented in the main article.
`Threads`	CPLEX parameter, number of cores that CPLEX is allowed to use. Default is 0 (automatic).
`timeLimit`	CPLEX parameter, time limit per problem provided to CPLEX. Default is 1e75 (infinite time).
`verbose`	print progress, different levels: 1) print simple progress. 2) print result of blocks. 3) print each k in blocks Default is FALSE.
`seed`	set seed for random number generator for the block strategy. Default is system default.
`warmstart`	warmstart for CPLEX or use a different problem for each k. Default is False.
`TH_IC`	is the ratio over one that the information criterion must increase to be STOP. Default is 1e-3.
`indexSelected`	array of pre-selected variables. WARNING: debug feature.

Compute the BOSO for use one block. This function calls cplexAPI to solve the optimization problem

A 'BOSO' object which contains the following information:

`betas`	estimated betas
`x`	trianing x set used in BOSO (input parameter)
`y`	trianing x set used in BOSO (input parameter)
`xval`	validation x set used in BOSO (input parameter)
`yval`	validation x set used in BOSO (input parameter)
`nlambda`	nlambda used by 'BOSO' (input parameter)
`intercept`	if 'BOSO' has used intercept (input parameter)
`standardize`	if 'BOSO' has used standardization (input parameter)
`mx`	Mean value of each variable. 0 if data has not been standarized
`sx`	Standard deviation value of each variable. 0 if data has not been standarized
`my`	Mean value of output variable. 0 if data has not been standarized
`dfmax`	Maximum number of variables set to be used by 'BOSO' (input parameter)
`result.final`	list with the results of the final problem for each K
`errorTrain`	error in training set in the final problem
`errorVal`	error in Validation set in the final problem of used by
`lambda.selected`	lambda selected in the final problem of
`p`	number of initial variables
`n`	number of events in the training set
`nval`	number of events in the validation set
`blockStrategy`	index of variables which were stored in each iteration by 'BOSO' in the block strategy

Luis V. Valcarcel

  #This first example is a basic 
  #example of how to execute BOSO
  
  
  data("sim.xy", package = "BOSO")
  obj <- BOSO(x = sim.xy[['low']]$x,
              y = sim.xy[['low']]$y,
              xval = sim.xy[['low']]$xval,
              yval = sim.xy[['low']]$yval,
              IC = 'eBIC',
              nlambda=50,
              intercept= 0, standardize = 0,
              Threads=1, verbose = 3, seed = 2021)
  coef(obj)  # extract coefficients at a single value of lambda
  predict(obj, newx = sim.xy[['low']]$x[1:20, ])  # make predictions