R: Searches for a tight bound for lambda

test_lambda_bounds {genscore}

R Documentation

Searches for a tight bound for `\lambda_{\boldsymbol{K}}` that gives the empty or complete graph starting from a given lambda with a given step size

Description

Searches for the smallest lambda that gives the empty graph (if lower == FALSE) or the largest that gives the complete graph (if lower == TRUE) starting from the given lambda, each time updating by multiplying or dividing by step depending on the search direction.

Usage

test_lambda_bounds(
  elts,
  symmetric,
  lambda = 1,
  lambda_ratio = 1,
  step = 2,
  lower = TRUE,
  verbose = TRUE,
  tol = 1e-06,
  maxit = 10000,
  cur_res = NULL
)

Arguments

`elts`	A list, elements necessary for calculations returned by `get_elts()`.
`symmetric`	A string. If equals `"symmetric"`, estimates the minimizer `\mathbf{K}` over all symmetric matrices; if `"and"` or `"or"`, use the "and"/"or" rule to get the support
`lambda`	A number, the initial searching point for `\lambda_{\mathbf{K}}`.
`lambda_ratio`	A positive number (or `Inf`), the fixed ratio `\lambda_{\mathbf{K}}` and `\lambda_{\boldsymbol{\eta}}`, if `\lambda_{\boldsymbol{\eta}}\neq 0` (non-profiled) in the non-centered setting.
`step`	A number, the multiplicative constant applied to lambda at each iteration. Must be strictly larger than 1.
`lower`	A boolean. If `TRUE`, finds the largest possible lambda that gives the complete graph (a `lower` bound). If `FALSE`, finds the smallest possible lambda that gives the empty graph (an `upper` bound).
`verbose`	Optional. A boolean. If `TRUE`, prints out the lambda value at each iteration.
`tol`	Optional. A number, the tolerance parameter.
`maxit`	Optional. A positive integer, the maximum number of iterations in model fitting for each lambda.
`cur_res`	Optional. A list, current results returned from a previous lambda. If provided, used as a warm start. Default to `NULL`.

Value

`lambda`	A number, the best `lambda` that produces the desired number of edges. `1e-10` or `1e15` is returned if out of bound.
`cur_res`	A list, results for this `lambda`. May be `NULL` if `lambda` is out of bound.

Examples

# Examples are shown for Gaussian truncated to R+^p only. For other distributions
#   on other types of domains, please refer to \code{gen()} or \code{get_elts()}, as the
#   way to call this function (\code{test_lambda_bounds()}) is exactly the same in those cases.
n <- 50
p <- 30
domain <- make_domain("R+", p=p)
mu <- rep(0, p)
K <- diag(p)
x <- tmvtnorm::rtmvnorm(n, mean = mu, sigma = solve(K),
       lower = rep(0, p), upper = rep(Inf, p), algorithm = "gibbs",
       burn.in.samples = 100, thinning = 10)

h_hp <- get_h_hp("min_pow", 1, 3)
dm <- 1 + (1-1/(1+4*exp(1)*max(6*log(p)/n, sqrt(6*log(p)/n))))
elts_gauss_np <- get_elts(h_hp, x, setting="gaussian", domain=domain,
                 centered=FALSE, profiled=FALSE, diag=dm)
lambda_cur_res <- test_lambda_bounds(elts_gauss_np, "symmetric", lambda=1,
                  lambda_ratio=1, step=1.5, lower=TRUE, cur_res=NULL)
lambda_cur_res2 <- test_lambda_bounds(elts_gauss_np, "symmetric", lambda=1,
                  lambda_ratio=1, step=1.5, lower=FALSE, cur_res=lambda_cur_res$cur_res)