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

Implementation of SVM

The one-class SVM algorithm does not use (ignores) the examples that are far from or deviated from the observations during training. Only the observations that are most concentrated or dense are leveraged for (unsupervised) learning and such an approach is effective in specific problems where very few deviations from normal are expected.

A synthetic dataset is created to implement SVM. We will have about 2% of the synthetic data in the minority class (outliers) denoted by 1 and 98% in the majority class (inliers) denoted by 0, and leverage the RBF kernel to map the data into a high-dimensional space. The Python code (with the scikit-learn library) runs as follows:

import pandas as pd, numpy as np
from collections import Counter
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.svm import OneClassSVM
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report
X, y = make_classification...