2. Linear Regression | F# for Machine Learning Essentials

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Table Of Contents

F# for Machine Learning Essentials

By : Sudipta Mukherjee

2 (1)

F# for Machine Learning Essentials

2 (1)

By: Sudipta Mukherjee

Overview of this book

The F# functional programming language enables developers to write simple code to solve complex problems. With F#, developers create consistent and predictable programs that are easier to test and reuse, simpler to parallelize, and are less prone to bugs. If you want to learn how to use F# to build machine learning systems, then this is the book you want. Starting with an introduction to the several categories on machine learning, you will quickly learn to implement time-tested, supervised learning algorithms. You will gradually move on to solving problems on predicting housing pricing using Regression Analysis. You will then learn to use Accord.NET to implement SVM techniques and clustering. You will also learn to build a recommender system for your e-commerce site from scratch. Finally, you will dive into advanced topics such as implementing neural network algorithms while performing sentiment analysis on your data.

Preface

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Free Chapter

1. Introduction to Machine Learning

1. Introduction to Machine Learning

Objective

Why use F#?

Unsupervised learning

Machine learning frameworks

Machine learning for fun and profit

Recognizing handwritten digits – your "Hello World" ML program

Summary

2. Linear Regression

2. Linear Regression

Objective

Different types of linear regression algorithms

APIs used

The basics of matrices and vectors (a short and sweet refresher)

QR decomposition of a matrix

Linear regression method of least square

Finding linear regression coefficients using F#

Finding the linear regression coefficients using Math.NET

Putting it together with Math.NET and FsPlot

Multiple linear regression

Multiple linear regression and variations using Math.NET

Weighted linear regression

Plotting the result of multiple linear regression

Ridge regression

Multivariate multiple linear regression

Feature scaling

Summary

3. Classification Techniques

3. Classification Techniques

Objective

Different classification algorithms you will learn

Some interesting things you can do

Understanding logistic regression

Multiclass classification using logistic regression

Multiclass classification using decision trees

Predicting a traffic jam using a decision tree: a case study

Challenge yourself!

Summary

4. Information Retrieval

4. Information Retrieval

Objective

Different IR algorithms you will learn

What interesting things can you do?

Information retrieval using tf-idf

5. Collaborative Filtering

5. Collaborative Filtering

Objective

Different classification algorithms you will learn

Vocabulary of collaborative filtering

Baseline predictors

Item-item collaborative filtering

Top-N recommendations

Evaluating recommendations

Ranking accuracy metrics

Working with real movie review data (Movie Lens)

Summary

6. Sentiment Analysis

6. Sentiment Analysis

Objective

What you will learn

A baseline algorithm for SA using SentiWordNet lexicons

Handling negations

Identifying praise or criticism with sentiment orientation

Pointwise Mutual Information

Using SO-PMI to find sentiment analysis

Summary

7. Anomaly Detection

7. Anomaly Detection

Objective

Detecting point anomalies using IQR (Interquartile Range)

Detecting point anomalies using Grubb's test

Grubb's test for multivariate data using Mahalanobis distance

Chi-squared statistic to determine anomalies

Detecting anomalies using density estimation

Strategy to convert a collective anomaly to a point anomaly problem

Dealing with categorical data in collective anomalies

Summary

Index

Index

QR decomposition of a matrix

The general linear regression model calculation requires us to find the inverse of the matrix, which can be computationally expensive for bigger matrices. A decomposition scheme, such as QR and SVD, helps in that regard.

QR decomposition breaks a given matrix into two different matrices—Q and R, such that when these two are multiplied, the original matrix is found.

In the preceding image, X is an n x p matrix with n rows and p columns, R is an upper diagonal matrix, and Q is an n x n matrix given by:

Here, Q1 is the first p columns of Q and Q2 is the last n – p columns of Q.

Using the Math.Net method QR you can find QR factorization:

Just to prove the fact that you will get the original matrix back, you can multiply Q and R to see if you get the original matrix back:

let myMatAgain = qr.Q * qr.R

SVD of a matrix

SVD stands for Single Value Decomposition. In this a matrix, X is represented by three matrices (the definition of SVD is taken from Wikipedia).

Suppose M...

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Tech Concepts

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Programming languages

73

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