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 introduced ML models as problems of mathematical optimization or mathematical programming. We found out that an end-to-end ML project is the sum of multiple small optimization problems. We also gained knowledge about how businesses can unlock the true value of data upon leveraging mathematical models (primarily driven by mathematical equations) in addition to ML (driven by data) models. We learned that an ML model is predominantly a predictive tool and a mathematical model is a prescriptive one.

In the next chapter (which begins the next part of the book), we will take a meticulous look at a well-known algorithm called PCA, utilized in an unsupervised ML model fit to data with high dimensionality. It is a dimensionality reduction technique and one of the most tried and tested mathematical tools employing constrained optimization.