1. Discrete state spae stochastic modelling. Markov chains in discrete and continuous time, discrete event simulation, population models. Continuous space-discrete time MArkov Processes 2. Continuous stochastic modeling: Stochastic Differential Equations (SDEs), Numerical Algorithms for SDEs, Fokker Planck Equation, Ito and Stratonovich SDEs, Noise-Induced Transitions, Bounded Stochastic Processes, Nonlinear Fokker-Planck Equation as Model of Phase Transitions 3. Stochastic approximations: mean field, Langevin approximation, hybrid approximations. 4. Parameter estimation, ABC method and system design. Examples from systems biology, epidemiology, statistical physics, performance of computer networks, ecology.

Introduction to Machine Learning; examples and taxonomy; design, development, and assessment of a ML system. Main supervised learning approaches and assessment of the learned model. Introduction to unsupervised learning and cluster analysis. Introduction to text mining and sentiment analysis.

Asymptotic Equipartition Property and Shannon’s theorem. Entropy, mutual and relative information. Limit theorems for sums and extremes. Large deviation theory and distributions of maximal entropy. Elements of coding theory. Applications to statistical inference.

Il corso si suddivide in quattro parti. La prima affronta l'entanglement quantistico e la completa positività, con un focus sulle mappe completamente positive e sull'entropia di von Neumann. La seconda parte introduce la teoria dell'informazione classica, includendo concetti come l'entropia di Shannon e i teoremi di Shannon sulla capacità di trasmissione. La terza parte si concentra sull'entropia quantistica e sui canali quantistici, con discussioni sulle loro differenze e analogie con i concetti classici. Infine, l'ultima parte del corso esplora il machine learning, sia classico che quantistico, discutendo l'utilizzo degli aspetti quantistici come sovrapposizione lineare ed entangolamento degli stati.

Il corso si suddivide in due parti: nella prima, vengono introdotti i concetti fondamentali della computazione quantistica, come il qubit, i gate quantistici, gli algoritmi principali e si suggerisce di eseguire esercizi. Nella seconda parte, si esplorano diverse tecnologie per realizzare qubit quantistici, tra cui cavity QED, ioni intrappolati, qubit superconduttori e la computazione quantistica adiabatica. Ogni tecnologia viene esaminata per i suoi vantaggi e limitazioni, fornendo così una panoramica delle opzioni disponibili per la costruzione di computer quantistici.

Probabilistic and Bayesian linear regression and classification. Kernel based methods and Gaussian Processes. Graphical models and exact inference. Sampling methods. Approximate inference for models with latent variables. Generative modelling.

The course focuses on fundamental elements of statistical inference, along with some principles and statistical techniques useful for the analysis of complex data.

The course provides a thorough exploration of deep learning, covering topics from basic principles to advanced techniques such as convolutional neural networks, recurrent neural networks, attention models, and transformers. Through theoretical explanations and practical exercises, students gain a comprehensive understanding of deep learning algorithms, enabling them to tackle real-world problems and analyze representations in deep learning models effectively.