Professors: **ANDERS JONSSON, VICENÇ GÓMEZ, GERGELY NEU **

**Course description**

The course describes the basic mathematical formulations that underly machine learning, but the focus is on practical knowledge. In each session, a novel concept is first introduced. The students are then given the opportunity to solve practical exercises related to this concept, exercises that have to be completed outside of class and handed in at a later date.

**Evaluation**

The evaluation consists in six homeworks, two lab exercises and a final exam. The homeworks and the final exam are individual, while each lab exercise can be carried out in groups of two or (exceptionally) individually.

**Content**

**Lecture 1: Intro to Machine Learning (Gergely)**

What is machine learning? Motivate through practical examples. Introduce different fields of machine learning and discuss how they differ from one another. What can be learned from data?

**Lecture 2: Linear models, error and noise (Gergely)**

Introduction to linear classification and linear regression. What can we say about the error of a given hypothesis? How is learning affected by noise? How well do learned hypotheses generalize to unseen examples?

**Lecture 3: The bias-variance tradeoff and logistic regression (Gergely/Vicenç)**

The bias-variance tradeoff offers an alternative view of generalization. How close to the target can we get using the hypothesis set? How noisy will our final hypothesis be as a function of the sampled inputs? Introduction to logistic regression.

**Lecture 4: Overfitting, regularization and validation (Gergely)**

Introduction to overfitting. What are some of the techniques for alleviating overfitting?

**Lecture 5: Decision trees and neural networks (Gergely)**

Introduction to decision trees, algorithms for constructing decision trees. Introduction to neural networks, backpropagation and deep learning.

**Lecture 6: Support vector machines (Gergely/Vicenç)**

Introduction to support vector machines, kernel methods and constraint optimization.

**Lecture 7: Bayesian inference (Vicenç)**

Learning as Inference. Model comparison and Occam's Razor.

**Lecture 8: Probabilistic graphical models (Vicenç)**

Introduction to Bayesian networks and Markov Random fields. Message-passing algorithms for probabilistic inference.

Lecture 9: Online optimization (Gergely)

Markov Decision Processes: policies, value functions and the Bellman equations. The notion of optimality in MDPs. Temporal-difference and policy-gradient methods. Online learning in Markov Decision Processes.

**Lecture 10: Bandits and reinforcement learning (Gergely)**

Online learning under partial feedback. Non-stochastic bandits and the Exp3 algorithm. Stochastic bandits and the UCB algorithm.

**Bibliography**

Y. Abu-Mostafa, M. Magdon-Ismail & H-T Lin: Learning from Data.

C. Bishop: Pattern Recognition and Machine Learning.

D. MacKay: Information Theory, Inference, and Learning Algorithms.

R. Sutton & A. Barto: Reinforcement Learning: An Introduction.