Calcolare le probabilità

Nell'ultimo esercizio hai visto come stimare le medie e le proporzioni quando le probabilità sono fornite. L'obiettivo di questo esercizio è stimare le probabilità quando le medie e le proporzioni sono note. Supponi che le medie per i cluster 1 e 2 siano rispettivamente 10 e 50, e supponi che il cluster 1 rappresenti il 35 percento della popolazione.

Inoltre, poiché ci interessa solo la stima dei parametri, supponi che entrambe le sd siano 10. Il set di dati gaussian_sample è disponibile nel tuo workspace.

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Modelli di Mixture in R

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Istruzioni dell'esercizio

Crea un nuovo data frame chiamato gaussian_sample_with_probs con le stime delle probabilità per i cluster 1 e 2. A questo scopo, crea due nuove variabili chiamate prob_cluster1 e prob_cluster2. Ricorda di normalizzare (scalare) le probabilità.
Visualizza le prime 6 osservazioni di gaussian_sample_with_probs.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# 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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Questo esercizio fa parte del corso

Modelli di Mixture 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: Struttura dei modelli di mistura Exercise 2: Quale distribuzione di probabilità?Exercise 3: Dataset delle cifre scritte a mano Exercise 4: Stima dei parametri Exercise 5: Stima date le probabilità Exercise 6: Calcolare le probabilità

Esercizio in corso

Exercise 7: Algoritmo EM Exercise 8: Funzione di expectation Exercise 9: Funzione di massimizzazione Exercise 10: Applica i due passaggi Exercise 11: Traccia i cluster stimati

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`