Gaussian Mixture Model with a Uniform Noise Component

Fits, by maximum likelihood (EM), a Gaussian mixture with an additional uniform "noise" component of density `lambda0 / V` capturing outliers, as in the noise-component model of `mclust` (Banfield & Raftery 1993). Each observation's posterior probability of the noise component can be used as an outlier score.

Usage

uniformNoiseGMM(
  x,
  lambda = NULL,
  mu = NULL,
  sigma = NULL,
  lambda0 = NULL,
  V = NULL,
  tol = 1e-06,
  maxiter = 1000,
  verbose = FALSE,
  keep.data = FALSE
)

Arguments

x

`numeric(n)` - A numeric vector of observations

lambda

`numeric` - Vector of mixing proportions of each normal component

mu

`numeric` - Vector of means of each normal component

sigma

`numeric` - Vector of standard deviations of each normal component

lambda0

Initial mixing proportion of the uniform noise component. `sum(lambda) + lambda0` must be 1.

V

Hyper-volume of the data region; defaults to `max(x) - min(x)`.

tol

Convergence tolerance on the change in beta-likelihood.

maxiter

Max iteration.

verbose

Print iteration progress.

keep.data

Keep a copy of `x` in the returned object.

Value

A list with elements `lambda`, `mu`, `sigma`, `lambda0`, `V`, `l` (log-likelihood), `iter`, and `converged`. If `maxiter` is reached before convergence, the last iterate is returned with `converged = FALSE` and a warning.

Examples

set.seed(404)
x <- rnormix(100, c(0.25, 0.75), c(0, 4), c(1, 1))
x[which.max(x)] <- 20 # outlier
uniformNoiseGMM(x, c(0.2475, 0.7425), c(0, 4), c(1, 1), lambda0 = 0.01)
#> $lambda
#> [1] 0.2951481 0.6879136
#> 
#> $mu
#> [1] 0.3020328 4.0091712
#> 
#> $sigma
#> [1] 1.2468809 0.8471066
#> 
#> $lambda0
#> [1] 0.01693827
#> 
#> $V
#> [1] 22.17879
#> 
#> $l
#> [1] -196.0319
#> 
#> $iter
#> [1] 40
#> 
#> $converged
#> [1] TRUE
#>