Mathematics for Machine Learning

Course objectives

The course aims to give an introduction to the mathematical theory of machine learning, including learning algorithms and big data analysis. The main goal is to provide the student with the basic language and tools of machine learning, from the point of view of statistical learning theory. At the end of the course the student will be acquainted with the best known algorithms and, in particular, she/he will be able to: - Formulate a machine-learning problem as an inverse stochastic problem and master the basic mathematical notions and tools connected to it - Identify the most suitable model and/or algorithm among those discussed during the course for a given machine learning problem - Implement simple algorithms and apply them to synthetic and/or real data - Analyze the performance of various algorithms from the point of view of computational complexity and statistical accuracy

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ELENA AGLIARI Lecturers' profile

Program - Frequency - Exams

Course program
1. Introduction Motivations Review on probability and statistics 2. Basics of Probabilistic ML: intro to parameter estimation - Likelihood, prior, posterior, marginal likelihood - Parameter estimation via MLE, MAP, fully Bayesian inference - Examples (Gaussians) 3. Probabilistic linear regression - Gaussian likelihood and prior - Exponential family 4. Probabilistic models for classification - Logistic regression - Laplace approximation 5. Generative models for Supervised learning 6. Latent variable models 7. Variational inference, inference by sampling 8. Advanced methods: statistical mechanics of pattern recognition
Prerequisites
Basics of probability theory and of algebra.
Books
Sergios Theodoridis Machine Learning: A Bayesian and Optimization Perspective Academic Press, 2019
Frequency
Non mandatory
Exam mode
Oral examination on the whole program of the course
Bibliography
K.P. Murphy, Probabilisitic Machine Learning - An introduction, MIT press (2022). A.C.C. Coolen, R. Kühn, P. Sollich, Theory of Neural Information Processing Systems, Oxford Press (2005). C.M. Bishop, Neural Networks for Pattern Recognition, Oxford (1995). C.M. Bishop, Pattern Recognition and Machine Learning, Springer (2009). K.P. Murphy, Machine Learning - A Probabilistic perspective, MIT press (2012). Lecturer’s notes, available on classroom
Lesson mode
Classroom lectures, mainly on the blackboard, with the aid of slides and projection of numerical codes and simulations
  • Lesson code10603322
  • Academic year2025/2026
  • CourseMathematical Sciences for Artificial Intelligence
  • CurriculumSingle curriculum
  • Year3rd year
  • Semester2nd semester
  • SSDMAT/07
  • CFU6