dependentsimr (version 1.0.0.0)

match_with_spiked_wishart: Compute what spiked SD values will give you the desired top eigenvalues by iteratively solving

Description

Compute what spiked SD values will give you the desired top eigenvalues by iteratively solving

Usage

match_with_spiked_wishart(
  desired_eigenvalues,
  rank,
  num_observations,
  num_variables,
  population_sd = 1,
  num_iterations = 20,
  num_samples_per_iter = 300
)

Value

Fit values of spiked SDs that approximately match the desired eigenvalues

Arguments

desired_eigenvalues

Vector of top eigenvalues of sample covariance matrix that should be approximated

rank

number of 'spiked' dimensions to fit

num_observations

Number of observations (samples, columns) in the data matrix

num_variables

Number of variables (features, rows) in the data matrix

population_sd

Standard deviation for allnon-spiked dimensions

num_iterations

Number of iterations to perform to to optimize. Increase to get a closer fit

num_samples_per_iter

Number of eigenvalues to samples to estimate mean eigenvalues for each iteration. Increase to get a closer fit

Examples

# First, simulate a dataset with known true values to see if we can get close
true_spiked_sd <- c(500, 100)
num_variables <- 1000
num_observations <- 10-1
sampled_eigenvalues <- sample_spiked_wishart(true_spiked_sd, num_observations,
      num_variables, num_eigs=2)
# Fit some spiked SDs that give eigenvalues similar to sampled_eigenvalues
fit <- match_with_spiked_wishart(
    sampled_eigenvalues,
    rank=2,
    num_observations,
    num_variables,
    num_iterations=5,
    num_samples_per_iter=50
)
# fit$spiked_sd should now be close to giving the specified sampled_eigenvalues (in expectation)
# fit$spiked_sd won't match the original true_spiked_sd too closely since it only
# fits the single sample # that gave  sampled_eigenvalue
# fit$population_sd gives fit value for the population SD