Book Image

Mastering Machine Learning Algorithms. - Second Edition

By : Giuseppe Bonaccorso
Book Image

Mastering Machine Learning Algorithms. - Second Edition

By: Giuseppe Bonaccorso

Overview of this book

Mastering Machine Learning Algorithms, Second Edition helps you harness the real power of machine learning algorithms in order to implement smarter ways of meeting today's overwhelming data needs. This newly updated and revised guide will help you master algorithms used widely in semi-supervised learning, reinforcement learning, supervised learning, and unsupervised learning domains. You will use all the modern libraries from the Python ecosystem – including NumPy and Keras – to extract features from varied complexities of data. Ranging from Bayesian models to the Markov chain Monte Carlo algorithm to Hidden Markov models, this machine learning book teaches you how to extract features from your dataset, perform complex dimensionality reduction, and train supervised and semi-supervised models by making use of Python-based libraries such as scikit-learn. You will also discover practical applications for complex techniques such as maximum likelihood estimation, Hebbian learning, and ensemble learning, and how to use TensorFlow 2.x to train effective deep neural networks. By the end of this book, you will be ready to implement and solve end-to-end machine learning problems and use case scenarios.
Table of Contents (28 chapters)
26
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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 pdata:

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 wj = P(N = j) is the relative weight of the jth 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...