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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

Applications of PCA

PCA is one fundamental algorithm and forms the foundation of ML. It finds use in diverse areas such as noise reduction in images, classification of data in general, anomaly detection, and other applications in medical data correlation. We will explore a couple of widely used applications of PCA in this section.

The scikit-learn library in Python provides functions for PCA. The following example code shows how to leverage PCA for dimensionality reduction while developing a predictive model that uses a PCA projection as input. We will be using PCA on a synthetic dataset while fitting a logistic regression model for classification:

from sklearn.datasets import make_classification
from sklearn.model_selection import cross_val_score
from sklearn.model_selection import RepeatedStratifiedKFold
from sklearn.pipeline import Pipeline
from sklearn.decomposition import PCA
from sklearn.linear_model import LogisticRegression
from numpy import mean
from numpy import std...

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