Probability / Stats: The Foundations of Machine Learning

Explore dispersion as the measure of how far data deviate from the mean, explaining variance as the average squared distance and standard deviation as its square root.

Explore dispersion by generating uniform and normal data, compare means, variances, and standard deviations, and visualize how scale affects plots, leading into probability and likelihood.

Quantify chance and learn the foundations of probability through practical, rigorous concepts such as axioms, universe, independent events, and simple coin flip problems.

Simulate coin flips with code to estimate heads probability, using seeds for reproducible randomness and dictionaries to derive frequencies and probabilities.

Explore probability foundations, including mutual exclusivity, union and inclusion-exclusion, independence, and conditional probability, with practical examples and intuition for mastering machine learning basics.

Apply conditional probability and Bayes rule to update beliefs from prior to posterior using prior, likelihood, and normalization, with a disease test example and a preview of spam detection.

Apply Bayes rule to a real-world spam detection task using a Naive Bayes model for binary classification, computing P(spam), P(word|spam), and P(word) to decide if a message is spam.

Explore practical spam detection by preparing text data, applying stop-word removal and stemming, building a dictionary, and computing word probabilities to classify messages.

Explore counting techniques essential to probability, including counting with and without replacement, permutations and combinations, and how to compute totals using factorials.

Explain random variables by mapping dice outcomes to numbers, and show how discrete distributions and probabilities form frequency distributions and cumulative frequency distributions.

Explore how two random variables interact using a joint probability table, and learn to derive marginals by summing over outcomes, illustrated with bags and blue or green balls.

Explore distributions from the Bernoulli to the binomial, learn how probability density functions and complements model experiments with successes and failures, and apply the binomial distribution to count successes.

Explore how to generate and plot discrete distributions with Python and Seaborn, compare theory and data, and study binomial and Poisson models.

Explore how continuous random variables use likelihood over ranges, transform via mu and sigma to the standard normal distribution, and compare uniform and normal shapes.

Explore uniform and normal distributions, examining location and scale while visualizing samples and pdfs. Learn about exponential and beta distributions and the distinction between pdf and pmf.

Explore a sleep analysis case study using time offsets and Bayes rule to compute sleep likelihood, update priors with likelihoods, and visualize results with code.

Visualize joint distributions for continuous variables using histograms, 3D plots, and contour plots; learn normalization, binning, and converting to 2D representations to reveal most probable value pairs.

Explore how fixing one variable affects the distribution of another, understand independence versus dependence, and visualize with 3D/2D plots, contour plots, and covariance in a multivariate normal framework.

Learn to compute the expected value of discrete and continuous random variables by weighting outcomes and summing or integrating, and see how entropy relates to decision making in machine learning.

Discover entropy and information in machine learning, define bits, and see how minimizing entropy lowers the expected number of yes-no questions to identify outcomes.

Explore entropy and information gain to build a simple decision tree that classifies data with binary attributes, illustrating efficient learning on small datasets.

Explore Bayesian inference as the future of machine learning, starting with priors and Bayes' rule to update posteriors with data, quantifying uncertainty.

Learn to perform bayesian inference with PyMC3 by building a simple linear model, generating data with noise and outliers, and examining posterior probabilities and posterior predictive regression lines.