  This work in progress aims to provide a unified introduction to statistical
learning, building up slowly from classical models like the GMM and HMM to
modern neural networks like the VAE and diffusion models. There are today many
internet resources that explain this or that new machine-learning algorithm in
isolation, but they do not (and cannot, in so brief a space) connect these
algorithms with each other or with the classical literature on statistical
models, out of which the modern algorithms emerged. Also conspicuously lacking
is a single notational system which, although unfazing to those already
familiar with the material (like the authors of these posts), raises a
significant barrier to the novice's entry. Likewise, I have aimed to assimilate
the various models, wherever possible, to a single framework for inference and
learning, showing how (and why) to change one model into another with minimal
alteration (some of them novel, others from the literature).
  Some background is of course necessary. I have assumed the reader is familiar
with basic multivariable calculus, probability and statistics, and linear
algebra. The goal of this book is certainly not completeness, but rather to
draw a more or less straight-line path from the basics to the extremely
powerful new models of the last decade. The goal then is to complement, not
replace, such comprehensive texts as Bishop's \emph{Pattern Recognition and
Machine Learning}, which is now 15 years old.
