EStep: Steps of the EM algorithm for a Gaussian Mixture model
In GMCM: Fast Estimation of Gaussian Mixture Copula Models

Description Usage Arguments Value Author(s) References See Also Examples

Functions to perform the expectation and maximization steps of the EM algorithm for an multivariate Gaussian mixture model.

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EStep(x, theta)

MStep(x, kappa, meta.special.case = FALSE)

`x`	A matrix of observations where rows corresponds to features and columns to experiments.
`theta`	A list of parameters formatted as described in `rtheta`.
`kappa`	A matrix where the (i,j)'th entry is the probability that `x[i,]` belongs to the `j`'th component. Usually the returned value of `EStep`.
`meta.special.case`	Logical. If `TRUE`, the maximization step is performed under the special case of Li et. al. (2011). Default values is `FALSE`.

EStep returns a matrix of probabilities as kappa above.

MStep returns a list of parameters formatted as described in rtheta.

Anders Ellern Bilgrau <anders.ellern.bilgrau@gmail.com>

Li, Q., Brown, J. B. J. B., Huang, H., & Bickel, P. J. (2011). Measuring reproducibility of high-throughput experiments. The Annals of Applied Statistics, 5(3), 1752-1779. doi:10.1214/11-AOAS466

rtheta

set.seed(1)
sim <- GMCM:::SimulateGMMData(n = 100)
x <- sim$z
true.theta <- sim$theta
init.theta <- GMCM:::rtheta()  # Generate starting parameters

# Do one EM interation
es <- GMCM:::EStep(x, init.theta)
new.theta <- GMCM:::MStep(x, es)

# Compare current estimate with the true
new.theta
true.theta

$m
[1] 3

$d
[1] 2

$pie
[1] 0.3985892 0.1700000 0.4314108

$mu
$mu$comp1
[1]   2.518367 -14.419702

$mu$comp2
[1] 13.49153 12.89264

$mu$comp3
[1] -9.134789 -2.551115


$sigma
$sigma$comp1
          [,1]      [,2]
[1,]  15.74861 -10.11403
[2,] -10.11403  10.40673

$sigma$comp2
         [,1]     [,2]
[1,] 9.116592 6.215996
[2,] 6.215996 4.291918

$sigma$comp3
          [,1]      [,2]
[1,] 1.7401099 0.9229792
[2,] 0.9229792 3.2189655


$m
[1] 3

$d
[1] 2

$pie
     pie1      pie2      pie3 
0.2193406 0.3074170 0.4732425 

$mu
$mu$comp1
[1] 13.29799 12.72429

$mu$comp2
[1]   4.146414 -15.399500

$mu$comp3
[1] -9.285670 -2.947204


$sigma
$sigma$comp1
          [,1]     [,2]
[1,] 13.348429 8.850678
[2,]  8.850678 5.934935

$sigma$comp2
           [,1]       [,2]
[1,]  3.0665824 -0.3895294
[2,] -0.3895294  2.6192252

$sigma$comp3
          [,1]      [,2]
[1,] 1.9840226 0.4433423
[2,] 0.4433423 2.8292856