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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27
Index

Conditional probabilities and Bayes' theorem

If we have a probability space and two events A and B, the probability of A given B is called conditional probability, and it's defined as:

As the joint probability is commutative, that is, P(A, B) = P(B, A), it's possible to derive Bayes' theorem:

This theorem allows expressing a conditional probability as a function of the opposite one and the two marginal probabilities P(A) and P(B). This result is fundamental to many machine learning problems, because, as we're going to see in this and in the next chapters, normally it's easier to work with a conditional probability (for example, p(A|B)) in order to get the opposite (that is, p(B|A)), but it's hard to work directly with the probability p(B|A). A common form of this theorem can be expressed as:

Let's suppose that we need to estimate the probability of an event A given some observations B, or using the standard...