Book Image

Statistics for Machine Learning

By : Pratap Dangeti
Book Image

Statistics for Machine Learning

By: Pratap Dangeti

Overview of this book

Complex statistics in machine learning worry a lot of developers. Knowing statistics helps you build strong machine learning models that are optimized for a given problem statement. This book will teach you all it takes to perform the complex statistical computations that are required for machine learning. You will gain information on the statistics behind supervised learning, unsupervised learning, reinforcement learning, and more. You will see real-world examples that discuss the statistical side of machine learning and familiarize yourself with it. You will come across programs for performing tasks such as modeling, parameter fitting, regression, classification, density collection, working with vectors, matrices, and more. By the end of the book, you will have mastered the statistics required for machine learning and will be able to apply your new skills to any sort of industry problem.
Table of Contents (16 chapters)
Title Page
Credits
About the Author
About the Reviewer
www.PacktPub.com
Customer Feedback
Preface

Singular value decomposition - SVD


Many implementations of PCA use singular value decomposition to calculate eigenvectors and eigenvalues. SVD is given by the following equation:

Columns of U are called left singular vectors of the data matrix, the columns of V are its right singular vectors, and the diagonal entries of

are its singular values. Left singular vectors are the eigenvectors of the covariance matrix and the diagonal element of

are the square roots of the eigenvalues of the covariance matrix.

Before proceeding with SVD, it would be advisable to understand a few advantages and important points about SVD:

  • SVD can be applied even on rectangular matrices; whereas, eigenvalues are defined only for square matrices. The equivalent of eigenvalues obtained through the SVD method are called singular values, and vectors obtained equivalent to eigenvectors are known as singular vectors. However, as they are rectangular in nature, we need to have left singular vectors and right singular vectors...