get_elts_loglog_simplex: The R implementation to get the elements necessary for...
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get_elts_loglog_simplex

R Documentation

The R implementation to get the elements necessary for calculations for the log-log setting (a=0, b=0) on the p-simplex.

Description

The R implementation to get the elements necessary for calculations for the log-log setting (a=0, b=0) on the p-simplex.

Usage

get_elts_loglog_simplex(
  hdx,
  hpdx,
  x,
  setting,
  centered = TRUE,
  profiled_if_noncenter = TRUE,
  scale = "",
  diagonal_multiplier = 1
)

Arguments

`hdx`	A matrix, `h(\mathbf{x})` applied to the distance of x from the boundary of the domain, should be of the same dimension as `x`.
`hpdx`	A matrix, `h'(\mathbf{x})` applied to the distance of x from the boundary of the domain, should be of the same dimension as `x`.
`x`	An `n` by `p` matrix, the data matrix, where `n` is the sample size and `p` the dimension.
`setting`	A string, log_log or log_log_sum0. If log_log_sum0, assumes that the true K has row and column sums 0 (see the A^d model), so only the off-diagonal entries will be estimated; the diagonal entries will be profiled out in the loss), so elements corresponding to the diagonals of K will be set to 0, and the loss will be rewritten in the off-diagonal entries only.
`centered`	A boolean, whether in the centered setting (assume `\boldsymbol{\mu}=\boldsymbol{\eta}=0`) or not. Default to `TRUE`.
`profiled_if_noncenter`	A boolean, whether in the profiled setting (`\lambda_{\boldsymbol{\eta}}=0`) if non-centered. Parameter ignored if centered=TRUE. Default to `TRUE`.
`scale`	A string indicating the scaling method. Returned without being checked or used in the function body. Default to `"norm"`.
`diagonal_multiplier`	A number >= 1, the diagonal multiplier.

Details

For details on the returned values, please refer to get_elts_ab or get_elts.

Value

A list that contains the elements necessary for estimation.

`n`	The sample size.
`p`	The dimension.
`centered`	The centered setting or not. Same as input.
`scale`	The scaling method. Same as input.
`diagonal_multiplier`	The diagonal multiplier. Same as input.
`diagonals_with_multiplier`	A vector that contains the diagonal entries of `\boldsymbol{\Gamma}` after applying the multiplier.
`setting`	The same setting as in the function argument.
`g_K`	The `\boldsymbol{g}` vector. In the non-profiled non-centered setting, this is the `\boldsymbol{g}` sub-vector corresponding to `\mathbf{K}`.
`Gamma_K`	The `\boldsymbol{\Gamma}` matrix with no diagonal multiplier. In the non-profiled non-centered setting, this is the `\boldsymbol{\Gamma}` sub-matrix corresponding to `\mathbf{K}`.
`g_eta`	Returned in the non-profiled non-centered setting. The `\boldsymbol{g}` sub-vector corresponding to `\boldsymbol{\eta}`.
`Gamma_K_eta`	Returned in the non-profiled non-centered setting. The `\boldsymbol{\Gamma}` sub-matrix corresponding to interaction between `\mathbf{K}` and `\boldsymbol{\eta}`.
`Gamma_eta`	Returned in the non-profiled non-centered setting. The `\boldsymbol{\Gamma}` sub-matrix corresponding to `\boldsymbol{\eta}`.
`t1,t2`	Returned in the profiled non-centered setting, where the `\boldsymbol{\eta}` estimate can be retrieved from `\boldsymbol{t_1}-\boldsymbol{t_2}\hat{\mathbf{K}}` after appropriate resizing.

Examples

n <- 50
p <- 30
eta <- rep(0, p)
K <- -cov_cons("band", p=p, spars=3, eig=1)
diag(K) <- diag(K) - rowSums(K) # So that rowSums(K) == colSums(K) == 0
eigen(K)$val[(p-1):p] # Make sure K has one 0 and p-1 positive eigenvalues
domain <- make_domain("simplex", p=p)
x <- gen(n, setting="log_log_sum0", abs=FALSE, eta=eta, K=K, domain=domain,
       xinit=NULL, seed=2, burn_in=1000, thinning=100, verbose=FALSE)
h_hp <- get_h_hp("min_pow", 2, 3)
h_hp_dx <- h_of_dist(h_hp, x, domain) # h and h' applied to distance from x to boundary

elts_simplex_0 <- get_elts_loglog_simplex(h_hp_dx$hdx, h_hp_dx$hpdx, x,
       setting="log_log", centered=FALSE, profiled=FALSE, scale="", diag=1.5)

# If want K to have row sums and column sums equal to 0; estimate off-diagonals only
elts_simplex_1 <- get_elts_loglog_simplex(h_hp_dx$hdx, h_hp_dx$hpdx, x,
       setting="log_log_sum0", centered=FALSE, profiled=FALSE, scale="", diag=1.5)
# All entries corresponding to the diagonals of K should be 0:
max(abs(sapply(1:p, function(j){c(elts_simplex_1$Gamma_K[j, (j-1)*p+1:p],
       elts_simplex_1$Gamma_K[, (j-1)*p+j])})))
max(abs(diag(elts_simplex_1$Gamma_K_eta)))
max(abs(diag(matrix(elts_simplex_1$g_K, nrow=p))))

genscore documentation built on May 31, 2023, 6:28 p.m.