1. Foundations of Probability Distributions
A probability distribution is a rule that assigns probabilities to outcomes in a sample space, with the total probability summing (for discrete cases) or integrating (for continuou...
Read full chapter →The essential Probability Distributions for ML cheat sheet: 8 concise chapters you can read in minutes, distilled from the full deck. When you're ready, drill the flashcards or test yourself under exam conditions.
A probability distribution is a rule that assigns probabilities to outcomes in a sample space, with the total probability summing (for discrete cases) or integrating (for continuou...
Read full chapter →A family of closely related discrete distributions arises from independent Bernoulli trials. The Bernoulli distribution itself models a single binary outcome: \(P(X = 1) = p\), \(P...
Read full chapter →Many continuous distributions arise from natural generative processes. The Uniform distribution on \([a, b]\) has constant density \(f(x) = 1/(b - a)\) over the interval, with mean...
Read full chapter →The Normal (Gaussian) distribution is the centerpiece of continuous probability for ML, with PDF \(f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)\...
Read full chapter →Parameter estimation can be framed either in frequentist or Bayesian terms. Maximum likelihood estimation (MLE) chooses parameters \(\theta\) to maximize the log-likelihood \(L(\th...
Read full chapter →Mixture distributions combine several component distributions to model data with heterogeneous structure: an index \(z\) is drawn from Categorical(\(\pi\)), then \(x\) is drawn fro...
Read full chapter →Classification algorithms can be organized by how they treat the joint distribution of features and labels. Generative classifiers model the joint \(p(x, y)\) by specifying \(p(y)\...
Read full chapter →When exact posterior computation is infeasible, Markov chain Monte Carlo (MCMC) provides a way to sample from a target distribution \(\pi\). A Markov chain satisfies the Markov pro...
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