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

Evolutionary optimization

Evolutionary optimization makes use of algorithms that mimic the selection process within the natural world. Examples of this are genetic algorithms that optimize via natural selection. Each iteration of a hyperparameter value is like a mutation in genetics that is assessed and altered. The process continues using recombined choices until the most effective configuration is reached. Hence, each generation improves with every iteration as it is optimized. Genetic algorithms are often used to train neural networks.

An evolutionary algorithm typically consists of three steps: initialization, selection, and termination. Fitter generations survive and proliferate, like in natural selection. In general, an initial population of a wide range of solutions is randomly created within the constraints of the problem. The population contains an arbitrary number of possible solutions to the problem, or the solutions are roughly centered around what is believed to be...