Statistical Analysis of Networks and Systems

Credits
6
Types
Specialisation compulsory (Computer Networks and Distributed Systems)
Requirements
This subject has not requirements , but it has got previous capacities
Department
AC
The course covers probabilistic foundations and the main families of deep generative models: VAEs, GANs, autoregressive models (Transformers), normalizing flows, flow matching (ODE/SDE), and diffusion models. Methods from deep reinforcement learning and Bayesian inference are also introduced. Designed for students with a background in discriminative machine learning.

Teachers

Person in charge

  • Jorge García Vidal (jorge@ac.upc.edu)

Others

  • Jose Maria Barceló Ordinas (jose.maria.barcelo@upc.edu)

Weekly hours

Theory
3.4
Problems
0.6
Laboratory
0
Guided learning
0
Autonomous learning
7.1

Competences

Technical Competences of each Specialization

Computer networks and distributed systems

  • CEE2.2 - Capability to understand models, problems and algorithms related to computer networks and to design and evaluate algorithms, protocols and systems that process the complexity of computer communications networks.

    • Generic Technical Competences

    Generic

  • CG4 - Capacity for general and technical management of research, development and innovation projects, in companies and technology centers in the field of Informatics Engineering.

    • Transversal Competences

    Appropiate attitude towards work

  • CTR5 - Capability to be motivated by professional achievement and to face new challenges, to have a broad vision of the possibilities of a career in the field of informatics engineering. Capability to be motivated by quality and continuous improvement, and to act strictly on professional development. Capability to adapt to technological or organizational changes. Capacity for working in absence of information and/or with time and/or resources constraints.

    • Basic

  • CB6 - Ability to apply the acquired knowledge and capacity for solving problems in new or unknown environments within broader (or multidisciplinary) contexts related to their area of study.

    • Objectives

    1. The main goal of the course is to develop in the students quantitative modeling skills, based on probabilistic techniques.
      Related competences: CB6, CTR5, CEE2.2, CG4,

    Contents

    1. Review of probability models and information theory
      Review of the probabilistic foundations required for the course: multivariate distributions, multivariate Gaussian, and key information theory concepts including entropy, conditional, entropy, cross-entropy, KL divergence (direct and reverse), and connection with maximum likelihood estimation.
    2. Deep generative models
      Introduction to deep generative models: models that learn to represent and sample from complex data distributions. We cover the main families: latent variable models (VAEs), GANs, autoregressive models based on Transformers, normalizing flows, and continuous generative models based on ODEs and SDEs, including flow matching and diffusion models. Theoretical foundations, differences in training and inference, and practical applications are discussed throughout.
    3. Reinforcement learning
      Introduction to deep reinforcement learning: agents that learn to make decisions through interaction with an environment. We cover the theoretical foundations (MDPs, Bellman equations, value functions), model-free methods such as Q-learning and DQN, and policy gradient methods including actor-critic and PPO. Connections with generative models and practical applications in complex, high-dimensional environments are discussed throughout.
    4. Bayesian methods
      Introduction to Bayesian methods applied to deep learning. We cover the foundations of Bayesian inference, the connection with variational inference introduced in the VAEs block, and practical methods for uncertainty quantification in neural networks such as Bayesian neural networks and Monte Carlo dropout. We discuss how to incorporate prior knowledge and obtain posterior distributions over model parameters.

    Activities

    Activity Evaluation act


    Review of probability models

    In-class activities (within the 4h theory block): problem solving on entropy and KL divergence calculations, discussion of practical cases on maximum likelihood estimation, and interactive visualization of multivariate Gaussians. Activities encourage active participation and build the probabilistic intuition required for subsequent blocks.
    Objectives: 1
    Contents:
    Theory
    4h
    Problems
    2h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Deep generative models

    In-class activities (within the 30h theory block): problem solving on the theoretical foundations of each model family (ELBO, minimax, change of variables, score matching), comparative discussion of training and inference differences across models, and analysis of experimental results from relevant papers. Activities combine mathematical rigour with intuition about the practical behaviour of the models.
    Objectives: 1
    Contents:
    Theory
    29.9h
    Problems
    4.1h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Reinforcement Learning

    In-class activities (within the 8h theory block): problem solving on MDPs and Bellman equations, discussion of practical cases on exploration and exploitation in complex environments, and comparative analysis of model-free methods (Q-learning, DQN) and policy gradient methods. Activities reinforce understanding of the theoretical foundations and connections with deep generative models.

    Theory
    8h
    Problems
    2h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Homework1



    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    25.9h

    Homework 2



    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    30h

    Bayesian methods

    In-class activities (within the 4h theory block): problem solving on Bayesian inference and computation of posterior distributions, discussion of the connection between variational inference and the VAE ELBO, and comparative analysis of practical uncertainty quantification methods such as Bayesian neural networks and Monte Carlo dropout.
    Objectives: 1
    Contents:
    Theory
    4h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Evaluation of basic concepts



    Week: 1
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Final evaluation



    Week: 1
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Evaluation of basic concepts



    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    10h

    Evaluation of basic concepts



    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    10h

    Teaching methodology

    Some materials will be posted online. The main results will be explained in the blackboard. Classes with problem solving and application examples.

    Evaluation methodology

    The evaluation is based on the development of 2 projects (each project is worth the same) and 4 short exams. The final grade for the course (FM) will be:
    FM = 0.6*(P1+P2)/2 + 0.1*Ex1 + 0.1*Ex2 + 0.1* Ex3 + 0.1 *Ex4.
    For each project, a research report is submitted where the proposed problem is analysed, the resolution methodology is described and the results and conclusions are described. Students will be assessed on their ability to demonstrate understanding and comprehension of the theory,
    ability to reason and communicate results .
    In the written exams (short exams at time class), they will be given a list of theoretical concepts related to the subject topics on which they have to demonstrate an understanding and comprehension. In the exam they will be asked to explain their understanding of these concepts.
    Weight of the generic competences in the evaluation of the specific part of the course
    25.0 % - Ability to apply the acquired knowledge and capacity for solving problems in new or unknown environments within broader (or multidisciplinary) contexts related to their area of study.
    25.0 % - Capability to communicate their conclusions, and the knowledge and rationale underpinning these, to both skilled and unskilled public in a clear and unambiguous way.
    50.0 % - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple
    experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation..

    Bibliography

    Basic

    Previous capacities

    Basic knowledge of probability theory, linear algebra and calculus, ML and neural networks