R: The constructor of a 'gips' class.

gips {gips}

R Documentation

The constructor of a `gips` class.

Description

Create a gips object. This object will contain initial data and all other information needed to find the most likely invariant permutation. It will not perform optimization. One must call the find_MAP() function to do it. See the examples below.

Usage

gips(
  S,
  number_of_observations,
  delta = 3,
  D_matrix = NULL,
  was_mean_estimated = TRUE,
  perm = ""
)

new_gips(
  list_of_gips_perm,
  S,
  number_of_observations,
  delta,
  D_matrix,
  was_mean_estimated,
  optimization_info
)

validate_gips(g)

Arguments

`S`	A matrix; empirical covariance matrix. When `Z` is the observed data: if one does not know the theoretical mean and has to estimate it with the observed mean, use `S = cov(Z)`, and leave parameter `was_mean_estimated = TRUE` as default; if one know the theoretical mean is 0, use `S = (t(Z) %*% Z) / number_of_observations`, and set parameter `was_mean_estimated = FALSE`.
`number_of_observations`	A number of data points that `S` is based on.
`delta`	A number, hyper-parameter of a Bayesian model. It has to be strictly bigger than 1. See the Hyperparameters section below.
`D_matrix`	Symmetric, positive-definite matrix of the same size as `S`. Hyper-parameter of a Bayesian model. When `NULL`, the (hopefully) reasonable one is derived from the data. For more details, see the Hyperparameters section below.
`was_mean_estimated`	A boolean. Set `TRUE` (default) when your `S` parameter is a result of a `stats::cov()` function. Set FALSE when your `S` parameter is a result of a `(t(Z) %*% Z) / number_of_observations` calculation.
`perm`	An optional permutation to be the base for the `gips` object. It can be of a `gips_perm` or a `permutation` class, or anything the function `permutations::permutation()` can handle. It can also be of a `gips` class, but it will be interpreted as the underlying `gips_perm`.
`list_of_gips_perm`	A list with a single element of a `gips_perm` class. The base object for the `gips` object.
`optimization_info`	For internal use only. `NULL` or the list with information about the optimization process.
`g`	Object to be checked whether it is a proper object of a `gips` class.

Value

gips() returns an object of a gips class after the safety checks.

new_gips() returns an object of a gips class without the safety checks.

validate_gips() returns its argument unchanged. If the argument is not a proper element of a gips class, it produces an error.

Functions

new_gips(): Constructor. It is only intended for low-level use.
validate_gips(): Validator. It is only intended for low-level use.

Methods for a `gips` class

Hyperparameters

We encourage the user to try D_matrix = d * I, where I is an identity matrix of a size ⁠p x p⁠ and d > 0 for some different d. When d is small compared to the data (e.g., d=0.1 * mean(diag(S))), bigger structures will be found. When d is big compared to the data (e.g., d=100 * mean(diag(S))), the posterior distribution does not depend on the data.

Taking D_matrix = d * I is equivalent to setting S <- S / d.

The default for D_matrix is D_matrix = d * I, where d = mean(diag(S)), which is equivalent to modifying S so that the mean value on the diagonal is 1.

In the Bayesian model, the prior distribution for the covariance matrix is a generalized case of Wishart distribution.

For a brief introduction, see the Bayesian model selection section in vignette("Theory", package = "gips") or in its pkgdown page).

For analysis of the Hyperparameters influence, see Section 3.2. of "Learning permutation symmetries with gips in R" by gips developers Adam Chojecki, Paweł Morgen, and Bartosz Kołodziejek, available on arXiv:2307.00790.

Examples

require("MASS") # for mvrnorm()

perm_size <- 5
mu <- runif(5, -10, 10) # Assume we don't know the mean
sigma_matrix <- matrix(
  data = c(
    1.0, 0.8, 0.6, 0.6, 0.8,
    0.8, 1.0, 0.8, 0.6, 0.6,
    0.6, 0.8, 1.0, 0.8, 0.6,
    0.6, 0.6, 0.8, 1.0, 0.8,
    0.8, 0.6, 0.6, 0.8, 1.0
  ),
  nrow = perm_size, byrow = TRUE
) # sigma_matrix is a matrix invariant under permutation (1,2,3,4,5)
number_of_observations <- 13
Z <- MASS::mvrnorm(number_of_observations, mu = mu, Sigma = sigma_matrix)
S <- cov(Z) # Assume we have to estimate the mean

g <- gips(S, number_of_observations)

g_map <- find_MAP(g, show_progress_bar = FALSE, optimizer = "brute_force")
g_map

summary(g_map)

if (require("graphics")) {
  plot(g_map, type = "both", logarithmic_x = TRUE)
}

[Package gips version 1.2.1 Index]

The constructor of a gips class.