Statistical Analysis of Networks and Systems

You are here

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 modeling techniques used in networking research. In particular it discusses discrete and continuous probability models, linear systems and system parameter estimation. 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 ( )

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: CB6, CTR5, CEE2.2, CG4,

Contents

  1. Discrete probability models
    Basic results. Examples: IQ switch max throughput, hash tables and ethernet switching. Anticolision methods in RFID tags. Bayesian antispam filters. Fountain codes.
  2. Continuous probability models
    Basic results. Exponential and Gaussian distribution. Residual times paradox. Large number laws. Law of Large Numbers and Central Limit theorem. Multivariate Gaussian distributions. Examples: Basic teletraffic models. Entropy, mutual information and coding theorem. Epidemic models in networks. Additive Gaussian Noise. Filtering smartphone sensor data.
  3. System parameter estimation
    Estimation problem. Graphical model and examples. Montecarlo methods.

Activities

Activity Evaluation act


Basic results of discrete probability

Review of basic discrete probability models. Concepat of independence and conditional probability. Combinatorial methods and basic models (Bernouilli, Binomial, Multinomial, Poisson).
Contents:
Theory
4h
Problems
4h
Laboratory
0h
Guided learning
0h
Autonomous learning
12h

Examples of discrete probability models

examples of discrete models applied to: switching systems, multiple access, reliability, etc
Contents:
Theory
4h
Problems
4h
Laboratory
0h
Guided learning
0h
Autonomous learning
12h

Basic results on continuous probability

Review of basic concepts of continuous probability models. Random variables, distributions and density functions. Basic models: exponential, gaussian, multivariate gaussian. Basic limit theorems results: Law of Large Numbers and Central Limit theorem.
Contents:
Theory
4h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
16h

Examples of continuous-probability models

Applications to: concept of entropy and mutual information. Coding theorem. Memoryless properties of the exponential distribution and examples of applications. Models for mobility in cellular networks.
Contents:
Theory
6h
Problems
4h
Laboratory
0h
Guided learning
0h
Autonomous learning
18h

Estimation of system parameters

We cover the theory of statisticsal estimation of system parameters, focusing on the bayesian approach. We start with a simple example (coin tossing), and then we introduce more complex examples, conjugacy, and the computational problems that appear in non-closed form solutions.
Contents:
Theory
6h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
12h

Graphical models and examples

We introduce some basic graphical model frameworks, DAGs and Markov Networks. We explain the concept of conditional independence with several examples. We intrdouce the message pasing technique exact and approximate) with application to decoding. We then adress two important examples: Kalman filters and Hidden Markov Models, with some application examples (e.g. location).
Contents:
Theory
4h
Problems
4h
Laboratory
0h
Guided learning
0h
Autonomous learning
16h

Montecarlo methods

We introduce the basic concepts behind Montecarlo in order to solve estimation problems without closed-form solutions. Importance sampling, Metropolis-Hastings and Gibbs sampling.
Contents:
Theory
4h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
10h

Teaching methodology

During the initial sessions of each theme, the main results will be explained in the blackboard. During the other sessions, will discuss in the classroom performance models taken from research papers.

Evaluation methodology

The evaluation is based on three different activities

- Programming homeworks(P)
- A detailed study of one paper (D)
- A final exam (E)

Each of the three activities will be evaluated (0=
The final mark for the course (F) will be:

F= 0.25xP+0.25xD+0.5xE

Bibliography

Basic:

Complementary:

Web links

Previous capacities

Basic knowledge of probability theory, linear algebra and calculus