Domain Neighborhood
Probability
Uncertainty made precise: events, random variables, expectations, and the distributions that models learn.
Recommended Route
Start here, then follow the prerequisites forward.
This sequence is ordered for learning rather than inventory: lower difficulty, fewer prerequisites, and more central concepts come first.
- 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.
- 02Distributions
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: both pages keep the probability thread active.
- 03Random 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: both pages keep the probability thread active.
- 04Cross-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: both pages keep the probability thread active.
- 05Maximum 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: both pages keep the probability / information theory thread active.
- 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: Bayesian Inference uses Maximum Likelihood directly.
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.
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.
Random Variables
A random variable is a function from outcomes to numbers; its distribution lets you compute expectations, variances, and likelihoods.
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.
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.
Bayesian Inference
Bayesian inference updates a prior distribution over unknowns into a posterior by multiplying by the likelihood and normalizing.