Book Image

Julia for Data Science

By : Anshul Joshi
2 (1)
Book Image

Julia for Data Science

2 (1)
By: Anshul Joshi

Overview of this book

Julia is a fast and high performing language that's perfectly suited to data science with a mature package ecosystem and is now feature complete. It is a good tool for a data science practitioner. There was a famous post at Harvard Business Review that Data Scientist is the sexiest job of the 21st century. (https://hbr.org/2012/10/data-scientist-the-sexiest-job-of-the-21st-century). This book will help you get familiarised with Julia's rich ecosystem, which is continuously evolving, allowing you to stay on top of your game. This book contains the essentials of data science and gives a high-level overview of advanced statistics and techniques. You will dive in and will work on generating insights by performing inferential statistics, and will reveal hidden patterns and trends using data mining. This has the practical coverage of statistics and machine learning. You will develop knowledge to build statistical models and machine learning systems in Julia with attractive visualizations. You will then delve into the world of Deep learning in Julia and will understand the framework, Mocha.jl with which you can create artificial neural networks and implement deep learning. This book addresses the challenges of real-world data science problems, including data cleaning, data preparation, inferential statistics, statistical modeling, building high-performance machine learning systems and creating effective visualizations using Julia.
Table of Contents (17 chapters)
Julia for Data Science
Credits
About the Author
About the Reviewer
www.PacktPub.com
Preface

Understanding matrixvariate distributions


This is a distribution from which any sample drawn is of type matrix. Many of the methods that can be used with Univariate and Multivariate distributions can be used with Matrix-variate distributions.

Wishart distribution

This is a type of matrix-variate distribution and is a generalization of the Chi-square distribution to two or more variables. It is constructed by adding the inner products of identically distributed, independent, and zero-mean multivariate normal random vectors. It is used as a model for the distribution of the sample covariance matrix for multivariate normal random data, after scaling by the sample size:

julia> Wishart(v, S) 

Here, v refers to the degrees of freedom and S is the base matrix.

Inverse-Wishart distribution

This is the conjugate prior to the covariance matrix of a multivariate normal distribution. In Julia, it is implemented as follows:

julia> InverseWishart(v, P) 

This represents an Inverse-Wishart...