Principles of Explainable Artificial Intelligence

Theory, Models & Proofs (Vol. 1)

Artificial Intelligence is transforming every sector of society, from healthcare and finance to autonomous systems and scientific discovery. However, as AI models become increasingly powerful, they also become more complex and less interpretable. Understanding why an AI model makes a particular decision has become one of the most important challenges in modern Artificial Intelligence.

Principles of Explainable Artificial Intelligence: Theory, Models & Proofs (Vol. 1) provides a comprehensive mathematical and practical introduction to Explainable Artificial Intelligence (XAI). The book bridges mathematics, statistics, optimization, causal inference, game theory, and machine learning to develop transparent, interpretable, and trustworthy AI systems.

Beginning with the fundamental concepts of explainability, transparency, interpretability, and fairness, the book introduces the mathematical foundations required to understand explainable machine learning, including linear algebra, probability theory, optimization, statistics, causal reasoning, and feature attribution.

Readers then explore advanced topics such as Structural Causal Models (SCMs), Directed Acyclic Graphs (DAGs), Pearl’s Do-Calculus, Shapley Values, SHAP algorithms, feature importance, statistical explainability, and game-theoretic interpretation, supported by mathematical derivations, proofs, and real-world examples.

Designed for undergraduate and postgraduate students, researchers, educators, AI professionals, and industry practitioners, this book combines theoretical rigor with practical AI applications to help build transparent, ethical, and reliable intelligent systems.

What You’ll Learn

✔ Explainable Artificial Intelligence (XAI)

✔ AI Transparency

✔ Model Interpretability

✔ Black-Box vs White-Box Models

✔ Local and Global Explanations

✔ Trustworthy AI

✔ Responsible AI

✔ Mathematical Foundations for XAI

✔ Set Theory

✔ Linear Algebra

✔ Vector Spaces

✔ Probability Theory

✔ Random Variables

✔ Statistical Expectations

✔ Variance Analysis

✔ Optimization Theory

✔ Gradient-Based Methods

✔ Distance Metrics

✔ Statistical Explainability

✔ Bias-Variance Tradeoff

✔ Feature Interaction Analysis

✔ Correlation and Covariance

✔ Uncertainty Quantification

✔ Hypothesis Testing

✔ Interpretable Statistical Models

✔ Linear Regression Interpretation

✔ Logistic Regression Interpretation

✔ Bayesian Explainability

✔ Regularization Techniques

✔ Causal Inference

✔ Correlation vs Causation

✔ Structural Causal Models (SCM)

✔ Directed Acyclic Graphs (DAGs)

✔ Pearl’s Causal Hierarchy

✔ Do-Calculus

✔ Backdoor Criterion

✔ Frontdoor Criterion

✔ Instrumental Variables

✔ Causal Discovery

✔ PC Algorithm

✔ FCI Algorithm

✔ GES Algorithm

✔ Granger Causality

✔ Causal Feature Selection

✔ Cooperative Game Theory

✔ Shapley Values

✔ Feature Attribution

✔ SHAP Framework

✔ Kernel SHAP

✔ Tree SHAP

✔ Deep SHAP

✔ Gradient SHAP

✔ Explainable Machine Learning

Part I – Foundations of Explainable Artificial Intelligence

Chapter 1

Introduction to Explainable Artificial Intelligence

Chapter 2

Mathematical Preliminaries

Part II – Statistical Foundations of Explainability

Chapter 3

Statistical Explainability

Chapter 4

Interpretable Statistical Models

Part III – Causality and Transparent Decision Systems

Chapter 5

Introduction to Causality

Chapter 6

Pearl’s Causal Framework

Chapter 7

Causal Discovery & Learning

Part IV – Mathematical Attribution & Shapley Values

Chapter 8

Game Theory Foundations

Chapter 9

Shapley Values — Theory & Properties

Chapter 10

SHAP Framework and Extensions

Who Should Read This Book?

This book is ideal for:

B.Tech Students
BCA Students
MCA Students
M.Tech Students
Artificial Intelligence Students
Machine Learning Engineers
Data Scientists
Deep Learning Researchers
Explainable AI Researchers
Computer Science Students
Statistics Students
Applied Mathematics Students
AI Engineers
Software Engineers
Research Scholars
University Faculty
Business Analytics Professionals
Healthcare AI Researchers
Responsible AI Practitioners
Competitive Examination Aspirants

Key Features

✅ Comprehensive introduction to Explainable Artificial Intelligence

✅ Mathematical foundations with detailed proofs

✅ Statistical and causal approaches to explainability

✅ SHAP and Shapley Value theory explained step by step

✅ Game Theory integrated with Machine Learning

✅ Causal inference and transparent decision-making

✅ Research-oriented and industry-relevant content

✅ Real-world case studies and practical AI applications

✅ University syllabus aligned

✅ Suitable for self-learning, research, graduate studies, and professional development

Why This Book?

Modern Artificial Intelligence systems increasingly influence critical decisions in healthcare, finance, autonomous vehicles, cybersecurity, and public policy. As these systems become more complex, transparency and interpretability become essential for building trustworthy AI.

Unlike traditional machine learning textbooks that focus primarily on predictive performance, Principles of Explainable Artificial Intelligence emphasizes understanding why AI models make decisions. By integrating mathematics, statistics, causal inference, optimization, and game theory, this book provides readers with a rigorous framework for designing transparent, interpretable, and responsible AI systems.

Whether you are conducting AI research, developing explainable machine learning models, or studying trustworthy Artificial Intelligence, this book offers both theoretical depth and practical guidance for mastering modern Explainable AI.

Book Details

Title: Principles of Explainable Artificial Intelligence

Subtitle: Theory, Models & Proofs

Volume: Vol. 1

Author: Anshuman Mishra

Publisher: Anshuman Mishra

Publication Year: 2025

Language: English

Category: Artificial Intelligence, Explainable AI, Machine Learning, Data Science, Statistics, Computer Science

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