EStep function

Steps of the EM algorithm for a Gaussian Mixture model

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

EStep(x, theta)

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

Arguments

• 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.

Returns

EStep returns a matrix of probabilities as kappa

above.

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

Examples

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

References

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

See Also

rtheta

Author(s)

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