Book Image

Practical Discrete Mathematics

By : Ryan T. White, Archana Tikayat Ray
Book Image

Practical Discrete Mathematics

By: Ryan T. White, Archana Tikayat Ray

Overview of this book

Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you’ll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you’ll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you’ll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
Table of Contents (17 chapters)
1
Part I – Basic Concepts of Discrete Math
7
Part II – Implementing Discrete Mathematics in Data and Computer Science
12
Part III – Real-World Applications of Discrete Mathematics

Chapter 10: Regression Analysis with NumPy and Scikit-Learn

The objective of this chapter is to predict an unknown variable based on samples of one or more other variables. In the simplest case, we have a sample of paired data (x1, y1), , (xn, yn) and need to find a line that best fits the data (that is, a line that passes through or is close to most of the data points) with SciPy implementations of the least-squares regression model. We will then extend the method to fit nonlinear curves and to take whole databases (x11, x12, …, x1k, y1), …,(xn1, xn2, …, xnk, yn) and try to predict y based on k input variables.

We will also be using some Python libraries, such as SciPy, NumPy, and scikit-learn. SciPy is an open source Python library for scientific computing, and NumPy will help us to work with multidimensional arrays and matrices and apply high-level mathematical functions to these arrays. Scikit-learn is a machine learning library, and we will be...