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

Optimization Techniques for Machine Learning

We discussed mathematical optimization techniques in the previous chapter and their necessity in business problems that require minimizing the cost (error) function and in predictive modeling, wherein the machine learns from historical data to predict the future. In Machine Learning (ML), the cost is a loss function or an energy function that is minimized. It can be challenging in most cases to know which optimization algorithm should be considered for a given ML model. Optimization is an iterative process to maximize or minimize an objective function and there is always a trade-off between the number of iteration steps taken and the computational hardship to get to the next step. In this chapter, hints of how to choose an optimization algorithm given a problem (hence, an objective) have been provided. The choice of optimization algorithm depends on different factors, including the specific problem to be solved, the size and complexity of...