Insegnamento a.a. 2026-2027

• Foundations of Bayesian Nonparametrics: exchangeability and de Finetti’s representation theorem.
• Nonparametric priors: definition, distributional properties and Bayesian nonparametric models.
• Computational methodologies for Bayesian Nonparametrics. Gradient-based sampling algorithms and diffusion models.
• Examples of Bayesian unsupervised learning: species sampling, mixture models, topic modeling in document analysis, probabilistic matrix factorization and tensor decomposition in networks and recommender systems.
• Supervised classification: Vapnik-Chervonenkis dimension, multi-layer perceptrons as universal approximators, regularized cross-entropy minimization as maximum a posteriori inference.
• Training: first order methods, reverse differentiation, initialization, covariate shift
• Regularization and data augmentation: weights and logits L2, dropout and stochastic depth, local entropy; mixup
• Introduction to PyTorch and computational aspects
• Specialized models and beyoond: convolutional networks, recurrent networks, attention mechanisms; generative models; reinforcement learning

• Have an overview of cutting-edge statistical and machine learning methods from a theoretical and methodological perspective.
• Understand the assumption and modeling implications underlying machine learning methodologies.
• Decide which method best fits a given problem.
• Understand the foundations of these methods in a way to allow to explain their implementations step by step.
• Understand the problems and pitfalls of testing and applying these methods.

• Design modern models for a given applied problem using Bayesian nonparametrics, Monte Carlo methods, neural networks, reinforcement learning or boosting.
• Understand the results in terms of the characteristics of the chosen method.

• Lectures

Face-to-face lectures.

The assessment consists of an individual presentation of a research paper or book chapter selected from a list provided by the instructors.The papers are related to the topics of the lectures and require knowledge of the models and methods covered during the course. The presentation is expected to demonstrate the students' theoretical and methodological understanding of the selected work, including its assumptions, modeling choices, inferential methods, and limitations. During the exam, students will also be asked questions on the relevant background material from the course.

Slides used during the lectures, containing extensive references to papers and book chapters, will be provided. In addition, a list of research papers for the final presentation will be made available.