OptimGumbelMixParams {pathwayPCA} | R Documentation

## Calculate the optimal parameters for a mixture of Weibull Extreme Value Distributions for supervised PCA

### Description

Calculate the parameters which minimise the negative log- likelihood of a mixture of two Weibull Extreme Value distributions.

### Usage

    OptimGumbelMixParams(
      max_tControl_vec,
      pathwaySize_vec,
      initialVals = c(p = 0.5, mu1 = 1, s1 = 0.5, mu2 = 1, s2 = 0.5),
      optimMethod = "L-BFGS-B",
      lowerBD = c(0, -Inf, 0, -Inf, 0),
      upperBD = c(1, Inf, Inf, Inf, Inf)
    )

### Arguments

`max_tControl_vec` | A vector of the maximum absolute t-scores for each pathway (returned by the `pathway_tControl` function) when under the null model. Under the null model, the response vector will have been randomly generated or parametrically bootstrapped.
`pathwaySize_vec` | A vector of the number of genes in each pathway.
`initialVals` | A named vector of initial values for the Weibull parameters. The values are p : The mixing proportion between the Gumbel minimum and Gumbel maximum distributions. This parameter is bounded by [0, 1] and defaults to 0.5. μ_1 : The mean of the first distribution. This parameter is unbounded and defaults to 1. s_1 : The precision of the first distribution. This parameter is bounded below by 0 and defaults to 0.5. μ_2 : The mean of the second distribution. This parameter is unbounded and defaults to 1. s_2 : The precision of the second distribution. This parameter is bounded below by 0 and defaults to 0.5.
`optimMethod` | Which numerical optimization routine to pass to the `optim` function. Defaults to `"L-BFGS-B"`, which allows for lower and upper bound constraints. When this option is specified, lower and upper bounds for ALL parameters must be supplied.
`lowerBD` | A vector of the lower bounds on the `initialVals`. Defaults to `c(0, -Inf, 0, -Inf, 0)`.
`upperBD` | A vector of the upper bounds on the `initialVals`. Defaults to `c(1, Inf, Inf, Inf, Inf)`.

### Details

The likelihood function is equation (4) in Chen et al (2008): a mixture of two Gumbel Extreme Value probability density functions, with mixing proportion p. Within the code of this function, the values `mu1`, `mu2` and `s1`, `s2` are placeholders for the mean and precision, respectively.

A computational note: the `"L-BFGS-B"` option within the `optim` function requires a bounded function or likelihood. We therefore replaced `Inf` with `10 ^ 200` in the check for boundedness. As we are attempting to minimise the negative log- likelihood, this maximum machine value is effectively `+Inf`.

See https://doi.org/10.1093/bioinformatics/btn458 for more information.

### Value

A named vector of the estimated values for the parameters which minimize the negative log-likelihood of the mixture Weibull Extreme Value distributions.

### See Also

`optim`; `GumbelMixpValues`; `pathway_tControl`; `SuperPCA_pVals`

### Examples

      # DO NOT CALL THIS FUNCTION DIRECTLY.
      # Use SuperPCA_pVals() instead.

    ## Not run:
      ###  Load the Example Data  ###
      data("colon_pathwayCollection")

      ###  Simulate Maximum Absolute Control t-Values  ###
      # The SuperPCA algorithm defaults to 20 threshold values; the example
      #   pathway collection has 15 pathways.
      t_mat <- matrix(rt(15 * 20, df = 5), nrow = 15)

      absMax <- function(vec){
        vec[which.max(abs(vec))]
      }
      tAbsMax_num <- apply(t_mat, 1, absMax)

      ###  Calculate Optimal Parameters for the Gumbel Distribution  ###
      OptimGumbelMixParams(
        max_tControl_vec = tAbsMax_num,
        pathwaySize_vec = lengths(colon_pathwayCollection$pathways)
      )

    ## End(Not run)

[Package pathwayPCA version 1.10.0 Index]