Book Image

Machine Learning Algorithms - Second Edition

Book Image

Machine Learning Algorithms - Second Edition

Overview of this book

Machine learning has gained tremendous popularity for its powerful and fast predictions with large datasets. However, the true forces behind its powerful output are the complex algorithms involving substantial statistical analysis that churn large datasets and generate substantial insight. This second edition of Machine Learning Algorithms walks you through prominent development outcomes that have taken place relating to machine learning algorithms, which constitute major contributions to the machine learning process and help you to strengthen and master statistical interpretation across the areas of supervised, semi-supervised, and reinforcement learning. Once the core concepts of an algorithm have been covered, you’ll explore real-world examples based on the most diffused libraries, such as scikit-learn, NLTK, TensorFlow, and Keras. You will discover new topics such as principal component analysis (PCA), independent component analysis (ICA), Bayesian regression, discriminant analysis, advanced clustering, and gaussian mixture. By the end of this book, you will have studied machine learning algorithms and be able to put them into production to make your machine learning applications more innovative.
Table of Contents (19 chapters)

Bayes' theorem

Let's consider two probabilistic events, A and B. We can correlate the marginal probabilities P(A) and P(B) with the conditional probabilities P(A|B) and P(B|A), using the product rule:

Considering that the intersection is commutative, the first members are equal, so we can derive Bayes' theorem:

In the general discrete case, the formula can be re-expressed considering all possible outcomes for the random variable A:

As the denominator is a normalization factor, the formula is often expressed as a proportionality relationship:

This formula has very deep philosophical implications, and it's a fundamental element of statistical learning. First of all, let's consider the marginal probability, P(A). This is normally a value that determines how probable a target event is, such as P(Spam) or P(Rain). As there are no other elements, this kind...