PROBABILISTIC MACHINE LEARN-ING FROM SCRATCH. Bayesian Methods, Graphical Models & Inference - Mir Hossain

What if machine learning models could explain uncertainty instead of hiding it?

Most modern machine learning books teach optimization first: define a loss, compute gradients, and train models. But probabilistic machine learning approaches the problem differently. It asks:

What should we believe, and how should those beliefs change when new data arrives?

PROBABILISTIC MACHINE LEARNING FROM SCRATCH is a rigorous, implementation-driven guide to Bayesian methods, graphical models, probabilistic inference, and modern uncertainty-aware AI systems. Designed for serious learners, graduate students, ML engineers, and researchers, this book builds the field from first principles with complete derivations and practical code implementations.

Inside this book, you will learn:

Bayesian probability and statistical inference
Conjugate priors and exponential family distributions
Bayesian linear and logistic regression
Gaussian processes and kernel methods
Directed and undirected graphical models
Exact inference and belief propagation
Markov Chain Monte Carlo (MCMC)
Variational inference and ELBO optimization
Hidden Markov Models and latent variable models
Mixture models and the EM algorithm
Variational Autoencoders (VAEs)
Bayesian neural networks
Normalizing flows and diffusion models
Calibration, uncertainty estimation, and probabilistic decision-making

Unlike many theoretical texts, this book emphasizes implementation and intuition alongside mathematics. Nearly every algorithm is developed step-by-step and implemented using plain NumPy so readers understand not only how to use probabilistic methods, but why they work.

This book is ideal for:

Machine learning engineers
AI researchers
Data scientists
Graduate students
Advanced undergraduate students
Readers transitioning from classical ML into Bayesian AI

If you want to move beyond black-box models and truly understand uncertainty, inference, and probabilistic reasoning in machine learning, this book provides the mathematical foundation and practical skills to do it.