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Switch Between Parameter Spaces

Source: R/parameter_spaces.R
ParameterSpaces.Rd

This R6 object manages two related parameter spaces: the Optimization Space (for optimization) and the Interpretation Space (for easier interpretation).

In the Optimization Space, parameters are stored as a numeric vector, the standard format for numerical optimizers. Parameters in this space are typically identified.

In the Interpretation Space, parameters are stored as a list and can take different formats (e.g., matrix). Parameters here do not need to be identified.

The user can define transformation functions (not necessarily bijective) to switch between these two spaces via the $o2i() and $i2o() methods.

Methods

Public methods

Method new()

Initializes a new ParameterSpaces object.

Usage

ParameterSpaces$new(parameter_names, parameter_lengths_in_o_space)

Arguments

parameter_names

[character()]
Unique names for the parameters.

parameter_lengths_in_o_space

[integer()]
The length of each parameter in the optimization space.

Returns

A new ParameterSpaces object.

Method print()

Print an overview of the parameter spaces.

Usage

ParameterSpaces$print(show_transformer = FALSE)

Arguments

show_transformer

[logical(1)]
Show transformer functions in the output?

Method switch()

Switch between Optimization Space and Interpretation Space.

Usage

ParameterSpaces$switch(x, to = NULL)

Arguments

x

[numeric() | list()]
The parameters, either as a numeric vector (will be switched to Interpretation Space), or as a list() (will be switched to Optimization Space).

to

[character(1) | NULL]
Explicitly switch to a specific space, either

  • "o": Optimization Space

  • "i": Interpretation Space

If NULL, the function will switch to the other space.

Method o2i()

Define transformation functions when switching from Optimization Space to Interpretation Space.

Usage

ParameterSpaces$o2i(...)

Arguments

...

[function]
One or more transformation functions, named according to the parameters.

Transformers from Optimization Space to Interpretation Space (o2i) must receive a numeric. The default is the identity.

Method i2o()

Define transformation functions when switching from Interpretation Space to Optimization Space.

Usage

ParameterSpaces$i2o(...)

Arguments

...

[function]
One or more transformers functions, named according to the parameters.

Transformers from Interpretation Space to Optimization Space (i2o) must return a numeric. The default is as.vector().

Method clone()

The objects of this class are cloneable with this method.

Usage

ParameterSpaces$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

### Log-likelihood function of two-class Gaussian mixture model with
### parameter vector `theta` that consists of
### - `mu`, mean vector of length 2
### - `sd`, standard deviation vector of length 2, must be positive
### - `lambda`, class probability of length 1, must be between 0 and 1

normal_mixture_llk <- function(theta, data) {
  mu <- theta[1:2]
  sd <- exp(theta[3:4])
  lambda <- plogis(theta[5])
  c1 <- lambda * dnorm(data, mu[1], sd[1])
  c2 <- (1 - lambda) * dnorm(data, mu[2], sd[2])
  sum(log(c1 + c2))
}

### define parameter spaces
### - `mu` needs no transformation
### - `sd` needs to be real in optimization space and positive in
###    interpretation space
### - `lambda` needs to be real and of length `1` in optimization space, and
###    a probability vector of length `2` in interpretation space

normal_mixture_spaces <- ParameterSpaces$
  new(
    parameter_names = c("mu", "sd", "lambda"),
    parameter_lengths_in_o_space = c(2, 2, 1)
  )$
  o2i(
    "mu" = function(x) x,
    "sd" = function(x) exp(x),
    "lambda" = function(x) c(plogis(x), 1 - plogis(x))
  )$
  i2o(
    "mu" = function(x) x,
    "sd" = function(x) log(x),
    "lambda" = function(x) qlogis(x[1])
  )

### switch between parameter spaces

par <- list(                             # parameters in interpretation space
  "mu" = c(2, 4),
  "sd" = c(0.5, 1),
  "lambda" = c(0.4, 0.6)
)
(x <- normal_mixture_spaces$switch(par)) # switch to optimization space
#> [1]  2.0000000  4.0000000 -0.6931472  0.0000000 -0.4054651
normal_mixture_llk(
  theta = x, data = datasets::faithful$eruptions
)
#> [1] -382.1072
normal_mixture_spaces$switch(x)          # switch back
#> $mu
#> [1] 2 4
#> 
#> $sd
#> [1] 0.5 1.0
#> 
#> $lambda
#> [1] 0.4 0.6
#>