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

Gradient Descent

One optimization algorithm that lays the foundation for machine learning models is gradient descent (GD). GD is a simple and effective tool useful to train such models. Gradient descent, as the name suggests, involves “going downhill.” We choose a direction across a landscape and take whichever step gets us downhill. The step size depends on the slope (gradient) of the hill. In machine learning (ML) models, gradient descent estimates the error gradient, helping to minimize the cost function. Very few optimization methods are as computationally efficient as gradient descent. GD also lays the foundation for the optimization of deep learning models.

In problems where the parameters cannot be calculated analytically by use of linear algebra and must be searched by optimization, GD finds its best use. The algorithm works iteratively by moving in the direction of the steepest descent. At each iteration, the model parameters, such as coefficients in linear...