Calculating the probabilities

In the last exercise, you saw how you can estimate the means and proportions when the probabilities are provided. The aim of this exercise is to estimate the probabilities when the means and the proportions are known. Assume the means for cluster 1 and 2 are 10 and 50, respectively, and assume cluster 1 represents 35 percent of the population.

Also, since we are only concerned with the parameters' estimation, assume both sd are 10. The data set gaussian_sample is available for you in your workspace.

Diese Übung ist Teil des Kurses

Mixture Models in R

Anleitung zur Übung

Create a new data frame called gaussian_sample_with_probs with the estimations of the probabilities for cluster 1 and 2. For that purpose, create two new variables called prob_cluster1 and prob_cluster2. Remember to scale the probabilities.
Check out the first 6 observations of gaussian_sample_with_probs.

Interaktive Übung

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# Create data frame with probabilities
gaussian_sample_with_probs <- gaussian_sample %>% 
  ___(prob_from_cluster1 = 0.35 * ___(___, mean = 10, sd = 10),
         prob_from_cluster2 = 0.65 * dnorm(___, mean = 50, sd = 10),
         prob_cluster1 = ___/(prob_from_cluster1 + prob_from_cluster2),
         prob_cluster2 = ___/(prob_from_cluster1 + prob_from_cluster2)) %>%
  select(x, prob_cluster1, prob_cluster2) 
         
head(___)

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Diese Übung ist Teil des Kurses

Mixture Models in R

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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: Introduction to model-based clustering Exercise 2: Clustering approaches Exercise 3: Explore gender data Exercise 4: Gaussian distribution Exercise 5: Sampling a Gaussian distribution Exercise 6: (not so good) Estimations of the mean and sd Exercise 7: Gaussian mixture models (GMM)Exercise 8: Simulate a mixture of two Gaussian distributions Exercise 9: Plot histogram of Gaussian Mixture Exercise 10: Mixture of three Gaussian distributions

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

Aktuelle Übung

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`