Statistical Analysis of Networks and Systems

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Credits
6
Types
Specialization compulsory (Computer Networks and Distributed Systems)
Requirements
This subject has not requirements, but it has got previous capacities
Department
AC
The course covers some basic techniques used in statistical analysis of networks and systems. In particular it discusses discrete and continuous probability models, bayesian estimation, classification and regression, and graphical models and dynamic systems. These concepts are introduced through classical examples taken from different research areas, including traffic modelling, wireless transmission systems, smartphone sensor data filtering, switching systems, address lookup algorithms, optical switching, anti-spam filters, etc.

Teachers

Person in charge

  • Jorge García Vidal ( )

Others

  • Jose Maria Barceló Ordinas ( )

Weekly hours

Theory
2.4
Problems
1.6
Laboratory
0
Guided learning
0
Autonomous learning
7

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: CG4, CEE2.2, CB6, CTR5,

Contents

  1. Discrete probability models
    Probability axioms, basic combinatorics, random variables, independence and conditional probability, expected values (review, only problems and online material), inclusion/exclusion, conditional independence, inequalities (Markov, Chebyshev, Jensen), examples: Bernouilli, Binomial, Multinomial, Poisson, (weak) Law large numbers, entropy and mutual information.
  2. Continuous probability models
    Sigma-algebras, measures, examples of non-measureable sets, probability axioms (revisited), Real numbers: Borel sigma-algebra, Sequences: Cylinder sigma-algebra (optional, online material), Cumulative Distribution Functions, Density functions, examples: uniform, exponential, Gaussian (review, problems and online material), beta, dirichlet, (eigenvalues/eigenvectors, symmetric, positive definite matrices video), multivariate gaussian, memoryless of exponential distribution. Properties of Gaussian distributions, central limit theorem.
  3. Bayesian estimation, classification and regression
    Bernouilli variable: Maximum likelihood and bayesian estimation. Conjugate distributions. Bayesian classification and regression. Intro to MChs and MCMC (optional, online material)
  4. Graphical models and dynamic systems
    Graphical models. Belief propagation. Hidden Markov Models. Kalman filters. Time series

Activities

Activity Evaluation act


Discrete probability models

Review of basic discrete probability models. Inclusion/exclusion, conditional independence, inequalities (Markov, Chebyshev, Jensen), examples: Bernouilli, Binomial, Multinomial, Poisson, (weak) Law large numbers, entropy and mutual information
Objectives: 1
Contents:
Theory
6h
Problems
6h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Continuous probability models

Sigma-algebras, measures, examples of non-measureable sets, probability axioms, Real numbers: Borel sigma-algebra, Sequences: Cylinder sigma-algebra (optional, online material), Cumulative Distribution Functions, Density functions, examples: uniform, exponential, Gaussian (review, online material), beta, dirichlet, (eigenvalues/eigenvectors, symmetric, positive definite matrices, review online material), multivariate gaussian, memoryless of exponential distribution. Properties of Gaussian distributions, central limit theorem.
Objectives: 1
Contents:
Theory
6h
Problems
6h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Bayesian estimation, classification and regression

Bernouilli variable: Maximum likelihood and bayesian estimation. Conjugate distributions. Bayesian classification and regression. Intro to Markov Chains and MCMC (optional, online material)

Contents:
Theory
6h
Problems
6h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Graphical models & dynamic systems

Graphical models. Belief propagation. Hidden Markov Models. Kalman filters. Time series.
Objectives: 1
Contents:
Theory
6h
Problems
6h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

self-evaluating tests


Objectives: 1
Week: 4
Type: theory exam
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
17h

self-assesment test T2


Objectives: 1
Week: 8
Type: theory exam
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
17h

self assesment test T3


Objectives: 1
Week: 12
Type: theory exam
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
19h

self assesment test T4


Objectives: 1
Week: 16
Type: theory exam
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
19h

Homework1



Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
4.5h

Homework 2



Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
6h

Homework 3



Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
6h

Homework 4



Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
6h

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 two different activities

- 4 tests, one per each part of the course (Ai, i=1..4)
- 5 Homeworks (Ti, i=1..4, T5 is optional)

A= (1/4) Sum_i=1..4 Ai
T= (1/4) Sum_i=1..4 Ti + 1/5 x T5

Final mark of the course (F):

F = 0.5 xA + 0.5 T

Bibliography

Basic:

Complementary:

Web links

Previous capacities

Basic knowledge of probability theory, linear algebra and calculus

Addendum

Contents

No hi ha canvis respecte la guia docent. No changes regarding "guia docent"

Teaching methodology

Presencial (normalment el número de alumnes matriculats està per sota 20). Presential (normally the number of students registered is under 20)

Evaluation methodology

El mateix que el proposat a la guia docent. No changes regarding "guia docent"

Contingency plan

Es prepararien materials online per tota la assignatura. Classes per google meet per revisió dels conceptes més complexes i per problemes i dubtes (2 hores de classes per google meet a la setmana). We would post materials online for all the subject. Classes for google meet for review of the most complex concepts and for problems and questions (2 hours of classes for google meet per week)