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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

By : Ranja Sarkar, Dr. Ranja Sarkar
4.1 (7)
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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

4.1 (7)
By: Ranja Sarkar, 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)
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1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Summary

In this chapter, we learned about two linear algebraic methods used to reduce the dimensionality of data: namely, principal component analysis and linear discriminant analysis. The focus was on PCA, which is an unsupervised method to reduce the feature space of high-dimensional data and to know why this reduction is necessary for solving business problems. We did a detailed study of the mathematics behind the algorithm and how it works in ML models. We also learned about a couple of important applications of PCA along with the Python code.

In the next chapter, we will learn about an optimization method called Gradient Descent, which is arguably the most common (and popular) algorithm to optimize neural networks. It is a learning algorithm that works by minimizing a given cost function. As the name suggests, it uses a gradient (derivative) iteratively to minimize the function.

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