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

ML – a predictive tool

Working through a predictive model involves optimization at multiple steps on top of optimally fitting the learning algorithm to the data. It involves transforming raw data into a form most appropriate for consumption in learning algorithms. An ML model has hyperparameters that can be configured to tailor it to a specific dataset. It is a standard practice to test a suite of hyper-parameters for a chosen ML algorithm, which is called hyper-parameter tuning or optimization. A grid search or random search algorithm is used for such tuning. Figure 2.6 shows the two search algorithm types. Grid search is more suitable for a quick search of hyperparameters and is known to perform well in general. You can also use Bayesian optimization for hyper-parameter tuning in some problems. We will learn about these optimization techniques in detail in the last part of the book.

Figure 2.6: Grid search (L) versus random search (R)

Figure 2.6: Grid search (L) versus random search (R)

An ML practitioner...