Domain Neighborhood
Probability
Uncertainty made precise: events, random variables, expectations, and the distributions that models learn.
Start here. Predict once, then carry the invariant forward.
Xp(x)E[·]uncertaintyLearner lensWhat makes this domain feel navigable?
Take this lensStabilize the first mechanism, make one prediction, then move one node forward.
Recommended Route
Start here, then follow the prerequisites forward.
This sequence is ordered for learning rather than inventory. Published notebooks with an unavailable prerequisite—or a same-domain route step that depends on one—are labeled in the full inventory instead of being presented as ready steps.
- 01Probability Basics
Events are subsets of a sample space, and probabilities obey a few axioms; from there you get conditional probability, independence, and Bayes' rule.
12 mincodedemoentry pointEntry point: build the first mental model here.
- 02Random Variables
A random variable is a function from outcomes to numbers; its distribution lets you compute expectations, variances, and likelihoods.
14 mincodedemoafter Probability BasicsWhy this follows: Random Variables uses Probability Basics directly.
- 03Distributions
A distribution is the law of a random variable: it says how probability mass or density lands on the values the variable can take.
15 mincodedemoafter Random VariablesWhy this follows: Distributions uses Random Variables directly.
- 04Maximum Likelihood
Maximum likelihood fits parameters by making the observed data most probable; for classifiers it becomes negative log-likelihood, cross-entropy, and a KL fit to the empirical distribution.
18 mincodedemoafter Distributions, DerivativesWhy this follows: Maximum Likelihood uses Distributions directly.
- 05Cross-Entropy
Cross-entropy is the target-weighted surprise of a model distribution; in deep learning it is the bridge from likelihood to a differentiable training loss.
16 mincodedemoafter Maximum LikelihoodWhy this follows: Cross-Entropy uses Maximum Likelihood directly.
- 06Bayesian Inference
Bayesian inference updates a prior distribution over unknowns into a posterior by multiplying by the likelihood and normalizing.
17 mincodedemoafter Distributions, Maximum LikelihoodWhy this follows: both pages keep the probability thread active.
All Published Notebooks
Browse the territory.
Probability Basics
Events are subsets of a sample space, and probabilities obey a few axioms; from there you get conditional probability, independence, and Bayes' rule.
Random Variables
A random variable is a function from outcomes to numbers; its distribution lets you compute expectations, variances, and likelihoods.
Distributions
A distribution is the law of a random variable: it says how probability mass or density lands on the values the variable can take.
Maximum Likelihood
Maximum likelihood fits parameters by making the observed data most probable; for classifiers it becomes negative log-likelihood, cross-entropy, and a KL fit to the empirical distribution.
Cross-Entropy
Cross-entropy is the target-weighted surprise of a model distribution; in deep learning it is the bridge from likelihood to a differentiable training loss.
Bayesian Inference
Bayesian inference updates a prior distribution over unknowns into a posterior by multiplying by the likelihood and normalizing.