Book Image

A Handbook of Mathematical Models with Python

By : Dr. Ranja Sarkar
Book Image

A Handbook of Mathematical Models with Python

By: Dr. Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Summary

In this chapter, we explored SVM as a classifier. In addition to linear data, SVMs can efficiently classify non-linear data using kernel functions. The method used by the SVM algorithm can be extended to solve regression problems. SVM is utilized for novelty detection as well, wherein the training dataset is not polluted with outliers and the algorithm is exploited to detect a new observation as an anomaly, in which case the outlier is called a novelty.

The next chapter is about graph theory, a tool that provides the necessary mathematics to quantify and simplify complex systems. Graph theory is the study of relations (connections or edges) between a set of nodes or individual entities in a dynamic system. It is an integral component of ML and DL because graphs provide a means to represent a business problem as a mathematical programming task in the form of nodes and edges.