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)

Linear models for regression

Let's consider a dataset of real-value vectors drawn from a data generating process pdata:

Each input vector is associated with a real value yi:

A linear model is based on the assumption that it's possible to approximate the output values through a regression process based on this rule:

In other words, the strong assumption is that our dataset and all other unknown points lie in the volume defined by a hyperplane and random normal noise that depends on the single point. In many cases, the covariance matrix is Σ = σ2Im (that is, homoscedastic noise); hence, the noise has the same impact on all the features. Whenever this doesn't happen (that is, when the noise is heteroscedastic), it's not possible to simplify the expression of Σ. It's helpful to understand that this situation is more common than expected...