optimized_HUM {SCOR}

Optimizing Different Estimators Of Hyper Volume Under Manifold

Description

As we know 'SCOptim' is efficient in estimating maximizing Hyper Volume Under Manifolds Estimators, we made some pre-functions that optimizes specific Problems of EHUM,SHUM and ULBA.

Usage

optimized_EHUM(
  beta_start,
  labels,
  x_mat,
  rho = 2,
  phi = 0.001,
  max_iter = 50000,
  s_init = 2,
  tol_fun = 1e-06,
  tol_fun_2 = 1e-06,
  minimize = FALSE,
  time = 36000,
  print = FALSE,
  lambda = 0.001,
  parallel = TRUE
)

optimized_SHUM(
  beta_start,
  labels,
  x_mat,
  p = 0,
  rho = 2,
  phi = 0.001,
  max_iter = 50000,
  s_init = 2,
  tol_fun = 1e-06,
  tol_fun_2 = 1e-06,
  minimize = FALSE,
  time = 36000,
  print = FALSE,
  lambda = 0.001,
  parallel = TRUE
)

optimized_ULBA(
  beta_start,
  labels,
  x_mat,
  rho = 2,
  phi = 0.001,
  max_iter = 50000,
  s_init = 2,
  tol_fun = 1e-06,
  tol_fun_2 = 1e-06,
  minimize = FALSE,
  time = 36000,
  print = FALSE,
  lambda = 0.001,
  parallel = TRUE
)

Arguments

beta_start

The initial guess for optimum \beta by user

labels

Sample Sizes vector of that has number of elements in each category. It works like the labels of data matrix.

x_mat

The Data Matrix

rho

Step Decay Rate with default value 2

phi

Lower Bound Of Global Step Size. Default value is 10^{-6}

max_iter

Max Number Of Iterations In each Run. Default Value is 50,000.

s_init

Initial Global Step Size. Default Value is 2.

tol_fun

Termination Tolerance on the function value. Default Value is 10^{-6}

tol_fun_2

Termination Tolerance on the difference of solutions in two consecutive runs. Default Value is 10^{-6}

minimize

Binary Command to set SCOptim on minimization or maximization. FALSE is for minimization which is set default.

time

Time Allotted for execution of SCOptim

print

Binary Command to print optimized value of objective function after each iteration. FALSE is set fault

lambda

Sparsity Threshold. Default value is 10^{-3}

parallel

Binary Command to ask SCOptim to perform parallel computing. Default is set at TRUE.

p

This parameter exists for the case of optimized_SHUM only.p decides whether to use s_n(x) or \phi_n(x). p = 1 stands for \phi_n(x) and p = 0 stands for s_n(x)

Details

Optimization of EHUM, SHUM and ULBA using SCOptim.

Value

Optimum Values Of HUM Estimates

Examples

R <- optimized_SHUM(rep(1, 12), colnames(AL), AL, parallel = FALSE)
estimate_SHUM(R, colnames(AL), AL)
# This run will take about 10 mins on average based on computational capacity of the system
# Optimum value of HUM estimate noticed for this case : 0.8440681


R <- optimized_EHUM(rep(1, 12), colnames(AL), AL, parallel = FALSE)
estimate_EHUM(R, colnames(AL), AL)
# Optimum value of HUM estimate noticed for this case : 0.8403805

R <- optimized_ULBA(rep(1, 12), colnames(AL), AL, parallel = FALSE)
estimate_ULBA(R, colnames(AL), AL)
# Optimum value of HUM estimate noticed for this case : 0.9201903