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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

By : Ranja Sarkar, Dr. Ranja Sarkar
4.1 (7)
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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

4.1 (7)
By: Ranja Sarkar, 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)
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1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

ML as mathematical optimization

ML can be described as finding the unknown underlying (approximate) function that maps input examples to output examples. This is where the ML algorithm defines a parametrized mapping function and optimizes or minimizes the error in the function to find the values of its parameters. ML is function approximation along with function optimization. The function parameters are also called model coefficients. Each time we fit a model to a training dataset, we solve an optimization problem.

Each ML algorithm makes different assumptions about the form of the mapping function, which in turn influences the type of optimization to be performed. ML is a function approximation method to optimally fit input data. It is particularly challenging when the data (the size or the number of examples) is limited. An ML algorithm must be chosen in a way that it most efficiently solves an optimization problem; for example, SGD is used for neural nets, while ordinary least...

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