Saturday, 1 November 2025

Learning Theory from First Principles (Adaptive Computation and Machine Learning Series) (FREE PDF)

Python Developer November 01, 2025 Books, Machine Learning No comments

Introduction

Machine learning has surged in importance across industry, research, and everyday applications. But while many books focus on algorithms, code, and libraries, fewer dig deeply into why these methods work — the theoretical foundations behind them. Learning Theory from First Principles bridges this gap: it offers a rigorous yet accessible treatment of learning theory, showing how statistical, optimization and approximation ideas combine to explain machine-learning methods.

Francis Bach’s book is designed for graduate students, researchers, and mathematically-oriented practitioners who want not just to use ML, but to understand it fundamentally. It emphasises deriving results “from first principles”—starting with clear definitions and minimal assumptions—and relates them directly to algorithms used in practice.

Why This Book Matters

Many ML textbooks skip over deeper theory or bury it in advanced texts. This book brings theory front and centre, but ties it to real algorithms.
It covers a wide array of topics that are increasingly relevant: over-parameterized models, structured prediction, adaptivity, modern optimization methods.
By focusing on the simplest formulations that still capture key phenomena, it gives readers clarity rather than overwhelming complexity.
For anyone working in algorithm design, ML research, or seeking to interpret theoretical claims in contemporary papers, this book becomes a critical reference.
Because ML systems are increasingly deployed in high-stakes settings (medical, legal, autonomous), understanding their foundations is more important than ever.

FREE PDF : Learning Theory from First Principles (Adaptive Computation and Machine Learning series)

What the Book Covers

Here’s an overview of the major content and how it builds up:

Part I: Preliminaries

The book begins with foundational mathematical concepts:

Linear algebra, calculus and basic operations.
Concentration inequalities, essential for statistical learning.
Introduction to supervised learning: decision theory, risks, optimal predictors, no-free-lunch theorems and the concept of adaptivity.

These chapters prepare the reader to understand more advanced analyses.

Part II: Core Learning Theory

Major sections include:

Linear least squares regression: Analysis of ordinary least squares, ridge regression, fixed vs random design, lower bounds.
Empirical Risk Minimization (ERM): Convex surrogates, estimation error, approximation error, complexity bounds (covering numbers, Rademacher complexity).
Optimization for ML: Gradient descent, stochastic gradient descent (SGD), convergence guarantees, interplay between optimization and generalisation.
Local averaging methods: Non-parametric methods such as k-nearest neighbours, kernel methods, their consistency and rates.
Kernel methods & sparse methods: Representer theorem, RKHS, ridge regression in kernel spaces, ℓ1 regularisation and high-dimensional estimation.

These chapters delve into how learning algorithms perform, how fast they learn, and what governs their behaviour.

Part III: Special Topics

In the later chapters, the book tackles modern and emerging issues:

Over-parameterized models (e.g., “double descent”), interpolation regimes.
Structured prediction: problems where output spaces are complex (sequences, graphs, etc.).
Adaptivity: how algorithms can adjust to favourable structure (sparsity, low-rank, smoothness).
Some chapters on online learning, ensemble learning and high-dimensional statistics.

This makes the book forward-looking and applicable to modern research trends.

Who Should Read This Book?

This book is well-suited for:

Graduate students in machine learning, statistics or computer science who need a theory-rich text.
Researchers and practitioners who design ML algorithms and want to justify them mathematically.
Engineers working on high-stakes ML systems who need to understand performance guarantees, generalisation, and potential failure modes.
Self-learners with strong background in linear algebra, probability and calculus aspiring to deep theoretical understanding.

If you are brand‐new to ML with only minimal maths background, this book may feel challenging—but it could serve as a stretch goal.

How to Get the Most Out of It

Work through proofs: Many key results are proved from first principles. Don’t skip them—doing so deepens understanding.
Implement the experiments/code: The author provides accompanying code (MATLAB/Python) for many examples. Running them clarifies concepts.
Use small examples: Try toy datasets to test bounds, behaviours, and rates of convergence discussed in the text.
Revisit difficult chapters: For example sparse methods, kernel theory or over-parameterisation may need multiple readings.
Reference when reading papers: When you encounter contemporary ML research, use this book to understand its theoretical claims and limitations.
Use it as a long-term reference: Even after reading, keep chapters handy for revisiting specific topics such as generalisation bounds, kernel methods, adaptivity.

Key Takeaways

Learning theory isn’t optional—it underpins why ML algorithms work, how fast, and in what regimes.
Decomposing error into approximation, estimation, and optimization is essential to understanding performance.
Modern phenomena (over-parameterisation, interpolation) require revisiting classical theory.
Theory and practice must align: the book emphasises algorithms used in real systems, not just idealised models.
Being comfortable with the mathematics will empower you to critically assess ML methods and deploy them responsibly.

Hard Copy: Learning Theory from First Principles (Adaptive Computation and Machine Learning series)

Kindle: Learning Theory from First Principles (Adaptive Computation and Machine Learning series)

Conclusion

Learning Theory from First Principles is a milestone book for anyone serious about mastering machine learning from the ground up. It offers clarity, rigour and relevance—showing how statistical, optimization and approximation theories combine to make modern ML work. Whether you’re embarking on research, designing algorithms, or building ML systems in practice, this book offers a roadmap and reference that will serve you for years.