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.
Jorge García Vidal (
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
CG4 - Capacity for general and technical management of research, development and innovation projects, in companies and technology centers in the field of Informatics Engineering.
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.
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.
The main goal of the course is to develop in the students quantitative modeling skills, based on probabilistic techniques.
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.
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.
System parameter estimation
Estimation problem. Graphical model and examples. Montecarlo methods.
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).
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.
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.
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.
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).