Gaussian mixture models (GMM)

Mixture Models in R

Victor Medina

Researcher at The University of Edinburgh

Flipping and sampling

Heads

Tails

# The number of observations
number_of_obs <- 500 
# Simulate the coin
coin <- sample(c(0,1), size = number_of_obs, 
                replace = TRUE, prob = c(0.5, 0.5)) 
head(coin)

0 1 0 1 0 0

table(coin)

coin
  0   1 
239 261

# Gaussian 1 "heads"
gauss_1 <- rnorm(n = number_of_obs, mean = 5, sd = 2)
# Gaussian 2 "tails"
gauss_2 <- rnorm(n = number_of_obs)

# Simulate the mixture
mixture_simulation <- ifelse(coin, gauss_1, gauss_2) 
head(cbind(coin, gauss_1, gauss_2, mixture_simulation))

     coin  gauss_1    gauss_2 mixture_simulation
[1,]    0 7.378712 -0.4559596         -0.4559596
[2,]    1 6.102770  3.3595880          6.1027696
[3,]    0 5.707269 -0.0731496         -0.0731496
[4,]    1 3.592059 -1.2407104          3.5920586
[5,]    0 5.236851 -0.5110058         -0.5110058
[6,]    0 4.152619 -0.5124031         -0.5124031

Plot the mixture

# Transform to a data frame
mixture_simulation <- data.frame(x = mixture_simulation)

# Create the histogram
ggplot(mixture_simulation) + 
     geom_histogram(aes(x = x, ..density..), bins = 40)

Changing the proportions

# Simulate the coin with different proportions
coin <- sample(c(0,1), size = number_of_obs, 
                replace = TRUE, prob = c(0.8, 0.2))

# Simulate the mixture
mixture_simulation <- data.frame(x = ifelse(coin, gauss_1, gauss_2))

# Create the histogram
ggplot(mixture_simulation) + 
   geom_histogram(aes(x = x, ..density..), bins = 40)

Mixture of three distributions

proportions <- sample(c(0, 1, 2), number_of_obs, 
                       replace = TRUE, prob = c(1/3, 1/3, 1/3))

gauss_3 <- rnorm(n = number_of_obs, mean = 10, sd = 1) 

mixture_simulation <- data.frame(x = ifelse(proportions == 0, gauss_1, 
                            ifelse(proportions == 1, gauss_2, gauss_3)))

ggplot(mixture_simulation) + 
   geom_histogram(aes(x = x, ..density..), bins = 40)

Let's practice!

Mixture Models in R