![[Solved] STAT542 Assignment 2](https://assignmentchef.com/wp-content/uploads/2022/08/downloadzip.jpg)
Implement the EM algorithm for a p-dimensional Gaussian mixture model with G components:
G
X
pk N(x;k,). k=1
Store the parameters as a list in R with three components
- prob: a G-dimensional probability vector;
- mean: a p-by-G matrix with the k-th column being k, the p-dimensional mean for the k-th Gaussian component;
- Sigma: a p-by-p covariance matrix shared by all G
Your code should have the following structure.
| Estep <- function(data, G, para){# Your Code# return the n-by-G probability matrix}Mstep <- function(data, G, para, post.prob){# Your Code# Return the updated parameters}myEM <- function(data, T, G, para){ for(t in 1:T){ post.prob <- Estep(data, G, para) para <- Mstep(data, G, para, post.prob)} return(para)} |
You should test your code on the faithful data from the R package mclust with G = 2. The estimated parameters from your algorithm and the one from mclust after T = 10 iterations should be the same.
| library(mclust)n <- nrow(faithful) Z <- matrix(0, n, 2)Z[sample(1:n, 120), 1] <- 1 Z[, 2] <- 1 Z[, 1]ini0 <- mstep(modelName=EEE, faithful, Z)$parameters# Output from my EM algpara0 <- list(prob = ini0$pro, mean = ini0$mean,Sigma = ini0$variance$Sigma)myEM(T=10, para=para0)# Output from mclustRout <- em(modelName = EEE, data = faithful, control = emControl(eps=0, tol=0, itmax = 10), parameters = ini0)$parameterslist(Rout$pro, Rout$mean, Rout$variance$Sigma) |
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