Book Image

Scala for Machine Learning - Second Edition

Book Image

Scala for Machine Learning - Second Edition

Overview of this book

The discovery of information through data clustering and classification is becoming a key differentiator for competitive organizations. Machine learning applications are everywhere, from self-driving cars, engineering design, logistics, manufacturing, and trading strategies, to detection of genetic anomalies. The book is your one stop guide that introduces you to the functional capabilities of the Scala programming language that are critical to the creation of machine learning algorithms such as dependency injection and implicits. You start by learning data preprocessing and filtering techniques. Following this, you'll move on to unsupervised learning techniques such as clustering and dimension reduction, followed by probabilistic graphical models such as Naïve Bayes, hidden Markov models and Monte Carlo inference. Further, it covers the discriminative algorithms such as linear, logistic regression with regularization, kernelization, support vector machines, neural networks, and deep learning. You’ll move on to evolutionary computing, multibandit algorithms, and reinforcement learning. Finally, the book includes a comprehensive overview of parallel computing in Scala and Akka followed by a description of Apache Spark and its ML library. With updated codes based on the latest version of Scala and comprehensive examples, this book will ensure that you have more than just a solid fundamental knowledge in machine learning with Scala.
Table of Contents (27 chapters)
Scala for Machine Learning Second Edition
Credits
About the Author
About the Reviewers
www.PacktPub.com
Customer Feedback
Preface
Index

Monte Carlo approximation


Monte Carlo experiments or sampling leverages randomness to solve mathematical or even deterministic problems [8:3]. There are three categories of problems:

  • Sampling from a given or empirical probability distribution

  • Optimization

  • Numerical approximation

This section focuses on the numerical integration.

Overview

Let's apply the Monte Carlo simulation to numerical integration. the goal is to compute the area under a given single variable function [8:4]. The method consists of the following three-step process:

  1. Define the outer area that is defined by the x axis and the maximum value of the function over the integration interval.

  2. Generate a uniformly random distributed data point {x, y} over the outer area.

  3. Count, then compute, the ratio of the number of data points under the function over the total number of random points.

The following diagram illustrates the three-step numerical integration for the function 1/x:

Monte Carlo numerical integration

Implementation

The MonteCarloApproximation...