Assumptions become models
See how a data-generating story determines the mathematics.
An interactive field guide to machine learning
See how models
learn.
Connect probability to inference, decisions, optimization, and neural networks. Change the assumptions. Watch the math respond. Understand why an algorithm works before memorizing how.
Uncertainty becomes action
Move from posterior beliefs to exploration and optimization.
Objectives become learning
Derive loss functions from likelihoods, then follow their gradients.
Learning paths
Follow the connections.
Start anywhere.
Follow the connections.
Each path combines derivation, visual intuition, and a client-side experiment. The chapters share one vocabulary so ideas reappear in new roles.
Foundation / 01
Probability models
Mechanisms, distributions, transformations, and limits.
Explore probability →Inference / 02Bayesian learning
Posterior updates, Thompson sampling, and Bayesian optimization.
Follow the posterior →Learning / 033 lessonsDeep learning
Activations, likelihood-derived objectives, and the architectures built from them.
Open deep learning →Learning / 04Semi-supervised learning
Use a few labels and many unlabeled examples without hiding the assumptions.
Propagate a label →Probability foundation
with assumptions about data.
Every model begins
with assumptions about data.
Choose a distribution and tune its parameters. These probability models return later as priors, likelihoods, output heads, and objective functions.
continuous
Normal
The central limit attractor and the default local model for additive noise.
f(x) = exp(−(x−μ)²/2σ²) / (σ√2π)Supportℝ
Mean0
Variance1
Recommended next chapter
Watch a posterior learn from evidence.
Start with a Beta prior, add observations one at a time, then turn that changing belief into Thompson sampling and Bayesian optimization.
Follow the posterior