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

Optimizing machine learning models

The concept of optimization is integral to an ML model. ML helps make clusters, detect anomalies, predict the future from historical data, and so forth. However, when it comes to minimizing costs in a business, finding optimal placement of business facilities, et cetera, what we need is a mathematical optimization model.

We will talk about optimization in machine learning in this section. Optimization ensures that the structure and configuration of the ML model are as effective as possible to achieve the goal it has been built for. Optimization techniques automate the testing of different model configurations. The best configuration (set of hyperparameters) has the lowest margin of error, thereby yielding the most accurate model for a given dataset. Getting the hyperparameter optimization right for an ML model can be tedious, as both under-optimized (underfit) as well as over-optimized (overfit) models fail. Overfitting is when a model is trained...