Youtor
R Tutorial Gaussian mixture models GMM
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=6f3wIQ0uAdM
Want to learn more? Take the full course at https://learn.datacamp.com/courses/mi... at your own pace. More than a video, you'll learn hands-on coding quickly apply skills to your daily work. • --- • Now that you have learned how to simulate observations from a Gaussian distribution, it is time to simulate a simple mixture of two Gaussian components. • To do so, we will imagine we have a coin and samples from two different Gaussian distributions. • We flip the coin and whenever comes up heads, we take a sample from the first Gaussian distribution, otherwise, we take a sample from the second Gaussian. For the moment, don't mind what are representing the Gaussians. • We repeat this procedure until we reach the desired number of samples. • To simulate the results from a coin, we use the function `sample()`, where the first argument is the vector of values from which to choose, the second is the number of items to choose, the third if the sampling should be with replacement or not, here we consider with. And the last is the vector of probability weights corresponding to each element of the vector being sampled. • Here, we simulate 500 coin tosses, representing the number 1 as heads and 0 as tails, both with equal probabilities. • Using the function `table()` we summarise the number of each result. • Once we have simulated the coin tosses, we proceed to simulate two different Gaussian distributions. • The first one with a mean of 5 and a standard deviation of 2. The second with a mean of 0 and sd of 1, which corresponds to the standard normal distribution, the default distribution for `rnorm()`. • Then, we create the object mixture underscore simulation , which takes the values from the first Gaussian when the coin comes up 1 or heads, and from the second when the coin comes up 0 or tails. • The table combines the results with the function `cbind` and shows the first six rows with the function head. Observe that the last column is the resulting mixture of two Gaussians. • To plot the histogram of the simulated mixture, we follow the same path as before, that is to say, we transform the object into a data frame and use geom_histogram(). • You can see from the plot that two peaks appear, each of them accounting for the same area. • Instead of having equal probabilities for each side of the coin as before, we give now more chances to the tails, then we would expect that the second peak on the last plot decreases. • To do it in R, we just change the weights in the prob argument. • Here, we give 0.8 to the number 0. • The mixture is then created as before. • In fact, from the plot, you can see that the second peak has decreased. • The probability weights represent the importance of the distributions that form the mixture. • If the weight for a particular distribution is high, the subpopulation explained by that distribution is important. • We can also incorporate as many distributions as we want into our mixture. In this example, we simulate a mixture of three Gaussians. • First, we create the proportions object, which is analogous to the flipping coin process but now with 3 outcomes. • Then, we include a third Gaussian option with a mean of 10 and an sd of 1. • To plot it, we use the geom_histogram as before. • From the plot, we see, as expected, three different peaks. • Now, it's your turn to simulate a mixture of Gaussian distributions. • #DataCamp #RTutorial #Mixture #Models
#############################
