Polimi · 2024/25
Machine Learning
From what it means to learn from data through to reinforcement learning — the full Politecnico di Milano Machine Learning course, rebuilt as an interactive, exam-focused study guide.
10 chapters~7 h reading 126 past-exam questions
After this course you can
- Derive and fit linear and logistic models, and read residuals to tell under- from over-fitting
- Select models with k-fold cross-validation and reason about the bias-variance tradeoff behind regularisation
- State the PAC-learning framework and bound sample complexity from VC dimension
- Apply the kernel trick and derive the max-margin SVM in both primal and dual form
- Formalise a sequential decision problem as an MDP and solve it with dynamic programming, Q-learning or SARSA
Syllabus
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Introduction
What it means for a machine to learn from data — the mindset shift, the vocabulary you'll carry through every later chapter, and the three big paradigms that organise the entire course.
low exam weight. 25 minutes reading. 3 past-exam questions. -
Linear Regression
The first real algorithm — and the one every later model is benchmarked against. Fit a line in closed form, buy curves with basis functions, read the geometry as a projection, and meet regularisation and the Bayesian view.
high exam weight. 38 minutes reading. 14 past-exam questions. -
Linear Classification
From predicting numbers to predicting labels. Why fitting a line to 0/1 targets fails, how decision-boundary geometry works, and the three classifiers that replace it — the perceptron, logistic regression, and softmax — all sharing one gradient.
high exam weight. 40 minutes reading. 17 past-exam questions. -
Model Selection
How to choose a model that works tomorrow, not just today. The bias–variance decomposition, honest error estimation with cross-validation, the curse of dimensionality and three ways to fight it, analytical criteria (AIC/BIC), and the ensembles — bagging and boosting — that bend the trade-off.
high exam weight. 45 minutes reading. 29 past-exam questions. -
PAC Learning & VC Dimension
How do we know a learner will generalise before we ever see a test set? PAC theory turns "it works on the training data" into a quantitative promise: version spaces, Haussler's bound, sample complexity, the agnostic Hoeffding bound, and the VC dimension that measures capacity when the hypothesis space is infinite — ending in structural risk minimisation.
high exam weight. 42 minutes reading. 12 past-exam questions. -
Kernel Methods
The kernel trick gives linear models non-linear superpowers without ever computing the feature map. The dual representation of ridge regression, valid kernels and Mercer's theorem, the kernel zoo (linear, polynomial, RBF), RBF networks and Nadaraya–Watson, and Gaussian processes with calibrated uncertainty — all from one idea: replace inner products with $k(\mathbf{x},\mathbf{x}')$.
medium exam weight. 46 minutes reading. 7 past-exam questions. -
Support Vector Machines
The decision boundary that does not just separate the data but separates it with the most breathing room possible. Maximum-margin geometry, the primal/dual quadratic programs and KKT, support vectors and sparsity, the kernel trick, the soft margin with slack and C, and the hinge-loss view that ties SVMs into the regularized-loss family.
medium exam weight. 46 minutes reading. 10 past-exam questions. -
Markov Decision Processes
The mathematical scaffolding for sequential decision-making — states, actions, rewards, and the Bellman view of optimality. The Markov property, the MDP tuple, discounting, policies, value functions, the Bellman expectation and optimality equations, and the contraction property that powers every algorithm to come.
medium exam weight. 46 minutes reading. 6 past-exam questions. -
Solving MDPs
From the Bellman equations to actual algorithms that produce an optimal policy. Dynamic programming, iterative policy evaluation, the policy-improvement theorem, policy iteration, value iteration, and the linear-programming view — three families of method, all driving the same fixed point into existence.
medium exam weight. 42 minutes reading. 4 past-exam questions. -
Reinforcement Learning
Learning to act when the world hands you no manual. From sampled experience to optimal policies — Monte Carlo, temporal-difference learning, TD(λ) and eligibility traces, SARSA, Q-learning, multi-armed bandits with UCB1 and Thompson Sampling, and the exploration-vs-exploitation tension that ties them all together.
high exam weight. 58 minutes reading. 24 past-exam questions.