AdaSubBoost: AdaSubBoost and RSubBoost
In chstaerk/SubBoost: Subspace Boosting With Multivariable Base-learners

This function implements the adaptive subspace boosting algorithm (AdaSubBoost) as well as random subspace boosting (RSubBoost).

AdaSubBoost(
  data,
  Iter,
  K = 100,
  q = 10,
  size.fixed = NULL,
  tau = 0.01,
  const = 0,
  savings = 1,
  U_C = 25,
  family = "normal",
  conservative = TRUE,
  update = "S",
  adaptive = TRUE,
  s_max = 20,
  nstop = Iter,
  automatic.stopping = TRUE,
  marginal.screening = FALSE,
  plotting = FALSE
)

`data`	should be a list with data$x as design matrix and data$y as response
`Iter`	iterations
`K`	parameter K - default is set to 100
`q`	parameter q - default is set to 10
`size.fixed`	default is set to NULL
`tau`	parameter tau - default is set to 0.01
`const`	parameter const - default is set to 0
`savings`	default is set to 1
`U_C`	parameter is set to 25
`family`	default is set to "normal"
`conservative`	default is set to TRUE
`update`	default is set to "S"
`adaptive`	default is set to TRUE (AdaSubBoost), for RSubBoost specify as FALSE
`s_max`	default is set to 20
`nstop`	default is set to Iter
`automatic.stopping`	default is set to TRUE
`marginal.screening`	default is set to FALSE
`plotting`	default is set to FALSE

### high-dimensional example (AdaSubBoost and RSubBoost)
# load "hdi" package for riboflavin data
require(hdi)

data(riboflavin)
n <- length(riboflavin$y)
p <- dim(riboflavin$x)[2]

# input data format:
# list with design matrix in data$x and response vector in data$y
data <- list()
data$x <- as.matrix(riboflavin$x)
data$y <- as.vector(riboflavin$y)

# constant (gamma) in EBIC
const <- 1

# expected search size
q <- 20

# adaptation parameter
K <- p/q

# maximum size for initial screening
s_max <- 15

# learning rate
tau <- 0.01

# (maximum) number of iterations
Iter <- 1000

# AdaSubBoost
set.seed(123)
output <- AdaSubBoost(data = data, Iter = Iter, const = const,
                      K = K, q = q, tau = tau, s_max = s_max)
output$selected # selected variables by AdaSubBoost
output$coef[names(output$selected)] # estimated non-zero coefficients by AdaSubBoost


# RSubBoost (no adaptation of sampling probabilites for base-learners)
set.seed(123)
outputRSub <- AdaSubBoost(data = data, Iter = Iter, const = const,
                          K = K, q = q, tau = tau, s_max = s_max,
                          adaptive = FALSE)
outputRSub$selected  # selected variables by RSubBoost
outputRSub$coef[names(outputRSub$selected)]