Campuran tiga distribusi Gaussian

Apa yang akan berubah jika kita memasukkan distribusi lain ke dalam simulasi? Anda akan melihat bahwa menambah jumlah komponen akan menyebarkan kepadatan massa untuk memasukkan distribusi tambahan, tetapi logikanya tetap mengikuti dari latihan sebelumnya.

Latihan ini adalah bagian dari kursus

Model Campuran di R

Petunjuk latihan

Buat assignments, yang mengambil nilai 0, 1, dan 2 dengan probabilitas masing-masing 0,3; 0,4; dan 0,3.
Data frame mixture mengambil sampel dari distribusi Gaussian dengan mean 5 dan sd 2 ketika assignments bernilai 1. Jika assignments bernilai 2, maka mean adalah 10 dan sd adalah 1. Jika tidak, gunakan distribusi normal baku.
Plot histogram dengan 50 bin.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

number_observations <- 1000

# Create the assignment object
assignments <- sample(
	c(0,1,2), size = number_observations, replace = TRUE, prob = c(0.3, ___, 0.3)
)

# Simulate the GMM with 3 distributions
mixture <- data.frame(
	x = ifelse(___ == 1, rnorm(n = number_observations, mean = ___, sd = ___), ifelse(assignments == 2, rnorm(n = number_observations, mean = ___, sd = ___), rnorm(n = ___)))
)

# Plot the mixture
mixture %>% 
  ggplot() + ___(aes(x = x, y = ..density..), ___ = ___)

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Model Campuran di R

SkillTag.level.intermediateSkillTag.label

4.8+

Mulai Kursus Gratis

In this chapter, you will be introduced to fundamental concepts in model-based clustering and how this approach differs from other clustering techniques. You will learn the generating process of Gaussian Mixture Models as well as how to visualize the clusters.

Exercise 1: Pengantar pengelompokan berbasis model Exercise 2: Pendekatan pengelompokan (clustering)Exercise 3: Jelajahi data gender Exercise 4: Distribusi Gaussian Exercise 5: Sampling a Gaussian distribution Exercise 6: (kurang baik) Estimasi mean dan sd Exercise 7: Model campuran Gaussian (GMM)Exercise 8: Mensimulasikan campuran dua distribusi Gaussian Exercise 9: Plot histogram Campuran Gaussian Exercise 10: Campuran tiga distribusi Gaussian

Latihan Saat Ini

In this chapter, you will be introduced to the main structure of Mixture Models, how to address different data with this approach and how to estimate the parameters involved. To accomplish the estimation, you will learn an iterative method called Expectation-Maximization algorithm.

Exercise 1: Structure of mixture models Exercise 2: Which probability distribution?Exercise 3: Handwritten digits dataset Exercise 4: Parameters estimation Exercise 5: Estimation given the probabilities Exercise 6: Calculating the probabilities Exercise 7: EM algorithm Exercise 8: Expectation function Exercise 9: Maximization function Exercise 10: Apply the two steps Exercise 11: Plot the estimated clusters

This chapter shows how to fit Gaussian Mixture Models in 1 and 2 dimensions with `flexmix` package. The data used is formed by 10.000 observations of people with their weight, height, body mass index and informed gender.

Exercise 1: Univariate Gaussian Mixture Models Exercise 2: Number of clusters Exercise 3: Number of parameters Exercise 4: Univariate Gaussian Mixture Models with flexmix Exercise 5: Univariate case with flexmix Exercise 6: Extracting Parameters for Univariate Case Exercise 7: Visualizing Univariate Gaussian Mixture Model Exercise 8: Compare the results Exercise 9: Bivariate Gaussian Mixture Models Exercise 10: Cross-term from covariance matrix Exercise 11: Parameters in the bivariate case Exercise 12: Bivariate Gaussian Mixture Models with flexmix Exercise 13: Fit the model with cross-terms Exercise 14: Get the components Exercise 15: Create the ellipses Exercise 16: Visualize the clusters

In this module, you will learn how Mixture Models extends to consider probability distributions different from the Gaussian and how these models are fitted with `flexmix`. The datasets used are handwritten digits images and the number of crimes in Chicago city. For the first dataset you will find clusters that summarize the handwritten digits and for the second dataset, you will find clusters of communities where is more or less dangerous to live in.

Exercise 1: Bernoulli Mixture Models Exercise 2: Binary images Exercise 3: How many values?Exercise 4: Bernoulli Mixture Models with flexmix Exercise 5: Handwritten digits with `flexmix`Exercise 6: Poisson Mixture Models Exercise 7: Discover the lambda Exercise 8: Sample from Poisson distribution Exercise 9: Poisson Mixture Models with flexmix Exercise 10: Crimes data with `flexmix`