Probabilistic Machine Learning

Probabilistic Prediction

1. Probabilistic PredictionOutputs as distributions: predicting uncertainty instead of pretending certainty.1–2 h
2. The Multivariate GaussianMean vector and covariance matrix: the ellipse geometry behind GDA, mixtures, Gaussian processes, Kalman filters, and diffusion.1–2 h
3. Density Estimation: Histograms and KernelsEstimating a distribution from samples, and the bandwidth choice that decides between spiky and oversmoothed.1–2 h

Fitting

1. LikelihoodHow probable is the data under these parameters? The question that fits models.1–2 h
2. Maximum Likelihood EstimationFitting as hill-climbing on likelihood: the parameters that make data most probable win.1–2 h
3. MAP and PriorsBeliefs before data: priors pull the fit, and ridge regression is a Gaussian prior in disguise.1–2 h

Bayesian

1. Bayesian ReasoningUpdating beliefs with evidence: prior times likelihood, renormalized.1–2 h
2. Conjugate Priors and Bayesian UpdatingBeta-Bernoulli and friends: priors that stay in the family after seeing data, making updating visible.1–2 h
3. Bayesian Linear Regression and the Posterior PredictiveA distribution over lines instead of one line: uncertainty that grows away from the data.1–2 h
4. Gaussian ProcessesPriors over functions defined by a kernel: Bayesian regression without a fixed parameter vector.1–2 h

Trust

1. CalibrationDo 70% predictions happen 70% of the time? Reading reliability honestly.1–2 h
2. Uncertainty: Aleatoric vs EpistemicNoise in the world vs ignorance in the model: two uncertainties, two remedies.1–2 h
3. Conformal PredictionDistribution-free prediction sets with guaranteed coverage from a held-out calibration set.1–2 h