You're reading from Mastering Machine Learning Algorithms Expert techniques for implementing popular machine learning algorithms, fine-tuning your models, and understanding how they work

Product type Paperback

Published in Jan 2020

Publisher Packt

ISBN-13 9781838820299

Length 798 pages

Edition 2nd Edition

Languages

Python

Tools

Keras

Concepts

Machine Learning

Authors (2):

Giuseppe Bonaccorso

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Table of Contents (28) Chapters

Preface

1. Machine Learning Model Fundamentals

2. Loss Functions and Regularization FREE CHAPTER

3. Introduction to Semi-Supervised Learning

4. Advanced Semi-Supervised Classification

5. Graph-Based Semi-Supervised Learning

6. Clustering and Unsupervised Models

7. Advanced Clustering and Unsupervised Models

8. Clustering and Unsupervised Models for Marketing

9. Generalized Linear Models and Regression

10. Introduction to Time-Series Analysis

11. Bayesian Networks and Hidden Markov Models

12. The EM Algorithm

13. Component Analysis and Dimensionality Reduction

14. Hebbian Learning

15. Fundamentals of Ensemble Learning

16. Advanced Boosting Algorithms

17. Modeling Neural Networks

18. Optimizing Neural Networks

19. Deep Convolutional Networks

20. Recurrent Neural Networks

21. Autoencoders

22. Introduction to Generative Adversarial Networks

23. Deep Belief Networks

24. Introduction to Reinforcement Learning

25. Advanced Policy Estimation Algorithms

26. Other Books You May Enjoy

27. Index

Gaussian Mixture

In Chapter 3, Introduction to Semi-Supervised Learning, we discussed the Generative Gaussian Mixture model in the context of semi-supervised learning. In this section, we're going to apply the EM algorithm to derive the formulas for the parameter updates.

Let's start considering a dataset X, drawn from a data-generating process p_data:

We assume that the whole distribution is generated by the sum of k Gaussian distributions so that the probability of each sample can be expressed as follows:

In the previous expression, the term w_j = P(N = j) is the relative weight of the j^th Gaussian, while are the mean and the covariance matrix. For consistency with the laws of probability, we also need to impose the following:

Unfortunately, if we try to solve the problem directly, we need to manage the logarithm of a sum and the procedure becomes very complex. However, we have learned that it's possible to use latent variables as helpers whenever...