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)

Discriminant analysis

Let's suppose we consider a multi-class classification problem where the conditional probability for a sample xi ∈ ℜm to belong to the yj class can be modeled as a multivariate Gaussian distribution (X is assumed to be made up of independent and identically distributed (i.i.d) variables with extremely low collinearities):

In this case, the class j is fully determined by the mean vector μj and the covariance matrix Σj. If we apply the Bayes' theorem, we can obtain the posterior probability p(yj|xi):

Considering the discussion of Gaussian Naive Bayes, it's not difficult to understand how it's possible to estimate μj and Σj using the training set, in fact, they correspond to the sample mean and covariance and can be easily computed in closed form.

Now, for simplicity, let's consider a binary problem...