get_elts_loglog_simplex {genscore}

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))))