Regression is one of the most fundamental and influential techniques in Artificial Intelligence, Machine Learning, Data Science, and Predictive Analytics. From forecasting stock prices and predicting disease risks to estimating customer behavior, autonomous system control, and intelligent recommendation engines, regression models form the mathematical foundation of intelligent decision-making.

Linear and Nonlinear Regression in Artificial Intelligence: Mathematical Foundations, Regularization Techniques & Predictive Modeling (Vol-I) is a comprehensive and application-oriented textbook that systematically explores the theory, mathematics, algorithms, and practical implementation of regression models used in modern AI systems.

Unlike traditional regression books that emphasize only statistical theory, this volume integrates mathematical foundations, optimization techniques, machine learning algorithms, explainable AI, probabilistic modeling, Python programming, and real-world case studies into a unified learning experience.

Beginning with the mathematical principles of vectors, matrices, probability, optimization, and statistics, the book gradually introduces linear regression, regularized models, nonlinear regression, generalized linear models, ensemble methods, Bayesian approaches, neural network regression, and scalable AI systems. Each concept is supported with intuitive explanations, mathematical derivations, Python implementations, and practical AI applications.

Designed for students, educators, researchers, and industry professionals, this book serves as both an academic textbook and a practical reference for predictive modeling using Artificial Intelligence.

What You Will Learn

✔ Fundamentals of Regression Analysis

✔ Regression in Artificial Intelligence

✔ Supervised Learning

✔ Predictive Analytics

✔ Mathematical Foundations

✔ Linear Algebra for AI

✔ Matrix Operations

✔ Vector Calculus

✔ Optimization Techniques

✔ Probability and Statistics

✔ Maximum Likelihood Estimation (MLE)

✔ Bayesian Statistics

✔ Simple Linear Regression

✔ Multiple Linear Regression

✔ Least Squares Estimation

✔ Gradient Descent

✔ Model Evaluation

✔ R² and Adjusted R²

✔ Hypothesis Testing

✔ Residual Analysis

✔ Multicollinearity

✔ Variance Inflation Factor (VIF)

✔ Ridge Regression (L2)

✔ Lasso Regression (L1)

✔ Elastic Net Regression

✔ Feature Selection

✔ Cross Validation

✔ Polynomial Regression

✔ Kernel Methods

✔ Logistic Regression

✔ Multiclass Classification

✔ Generalized Linear Models (GLM)

✔ Poisson Regression

✔ Gamma Regression

✔ Decision Tree Regression

✔ Random Forest Regression

✔ Gradient Boosting

✔ XGBoost

✔ LightGBM

✔ CatBoost

✔ Support Vector Regression (SVR)

✔ Neural Network Regression

✔ Multi-Layer Perceptron (MLP)

✔ Deep Learning for Regression

✔ Bayesian Regression

✔ Gaussian Process Regression

✔ Explainable AI (SHAP & LIME)

✔ Distributed Machine Learning

✔ Online Learning

✔ Regression with Big Data

✔ Python Programming

✔ NumPy

✔ Pandas

✔ Matplotlib

✔ Scikit-learn

✔ TensorFlow

✔ PyTorch

✔ End-to-End AI Projects

✔ Interview Preparation

Key Features

• Comprehensive coverage of linear and nonlinear regression techniques

• Strong mathematical foundation with intuitive explanations

• Complete coverage of regularization methods

• Modern AI regression algorithms explained in detail

• Practical Python implementation using industry-standard libraries

• Real-world AI case studies and predictive modeling examples

• Explainable AI techniques using SHAP and LIME

• Bayesian and probabilistic regression methods

• Advanced machine learning regression algorithms

• Hyperparameter optimization techniques

• Industry-oriented projects and interview preparation

• Suitable for university curriculum and professional learning

Table of Contents Highlights

Unit I – Foundations of Regression

Introduction to Regression
Regression in Artificial Intelligence
Mathematical Foundations
Linear Algebra
Matrix Calculus
Probability
Statistics
Maximum Likelihood Estimation
Bayesian Concepts

Unit II – Linear Regression Models

Simple Linear Regression
Multiple Linear Regression
Least Squares
Gradient Descent
Model Diagnostics
Ridge Regression
Lasso Regression
Elastic Net
Cross Validation

Unit III – Nonlinear Regression Models

Polynomial Regression
Basis Expansion
Logistic Regression
Multiclass Classification
Generalized Linear Models
Poisson Regression
Gamma Regression

Unit IV – Advanced AI Regression

Decision Tree Regression
Random Forest
Gradient Boosting
XGBoost
LightGBM
CatBoost
Support Vector Regression
Neural Network Regression
Deep Learning Regression

Unit V – Probabilistic Regression

Bayesian Regression
MAP vs MLE
Bayesian Ridge
Bayesian Lasso
Gaussian Process Regression
Kernel Functions
Predictive Uncertainty

Unit VI – AI Applications

Big Data Regression
Stochastic Gradient Descent
Online Learning
Distributed Machine Learning
Explainable AI
SHAP
LIME
Healthcare AI
NLP
Finance
Computer Vision
Time Series Forecasting

Unit VII – Python Implementation

NumPy
Pandas
Matplotlib
Scikit-learn
TensorFlow
PyTorch
Hyperparameter Optimization
GridSearchCV
RandomSearch
Optuna
End-to-End Projects
AI Interview Questions
Research Trends

Who Should Read This Book?

This book is ideal for:

BCA Students
MCA Students
B.Tech (Computer Science & IT)
M.Tech Students
M.Sc. Computer Science Students
Artificial Intelligence Students
Machine Learning Students
Data Science Students
Statistics Students
AI Researchers
PhD Scholars
Computer Science Faculty
Software Engineers
Data Analysts
Machine Learning Engineers
AI Professionals

Why This Book?

Regression lies at the heart of predictive Artificial Intelligence. Yet, many resources either emphasize mathematical statistics without practical implementation or focus only on machine learning libraries without explaining the underlying mathematical principles.

Linear and Nonlinear Regression in Artificial Intelligence (Vol-I) bridges this gap by integrating mathematical foundations, optimization theory, statistical modeling, machine learning algorithms, Python programming, and real-world AI applications into a single comprehensive resource.

From classical linear regression to advanced Bayesian methods, Gaussian Processes, ensemble learning, neural networks, and explainable AI, this book provides readers with both theoretical understanding and practical implementation skills required for modern predictive modeling.

Whether you are preparing for university examinations, research, technical interviews, AI projects, or professional machine learning careers, this book serves as a complete guide to regression techniques in Artificial Intelligence.

Suitable For

BCA
MCA
B.Tech (Computer Science & IT)
M.Tech
M.Sc. Computer Science
Artificial Intelligence Programs
Machine Learning Courses
Data Science Programs
Statistics Courses
Predictive Analytics Programs
Research Projects
Competitive Examinations (GATE, UGC-NET, PhD Entrance)
Academic Libraries
Professional AI Training

Book Details

Title: Linear and Nonlinear Regression in Artificial Intelligence

Subtitle: Mathematical Foundations, Regularization Techniques & Predictive Modeling (Vol-I)

Author: Anshuman Mishra

Language: English

Subject: Artificial Intelligence, Machine Learning, Regression Analysis, Predictive Analytics, Data Science

Level: Beginner to Advanced

Gamma Regression

Linear and Nonlinear Regression in Artificial Intelligenc VOL-1