Statistical Analysis of Networks and Systems

• Teachers
• Weekly hours
• Competences
• Objectives
• Contents
• Activities
• Teaching methodology
• Evaluation methodology
• Bibliography
• Web links
• Previous capacities
• Addendum

Teachers

Person in charge

• Jorge García Vidal ( )

Others

• Jose Maria Barceló Ordinas ( )

Weekly hours

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

Teaching methodology

Evaluation methodology

Bibliography

Basic:

• Information theory, inference, and learning algorithms - MacKay, D.J.C, Cambridge University Press, 2003. ISBN: 0521642981
  http://cataleg.upc.edu/record=b1269009~S1*cat
• An introduction to probability theory and its applications - Feller, W, John Wiley and Sons, 1968. ISBN: 0471257117
  http://cataleg.upc.edu/record=b1005063~S1*cat
• Probability and statistics: the science of uncertainty - Evans, M.J.; Rosenthal, J.S, W.H. Freeman and Company, 2010. ISBN: 9781429224628
  http://cataleg.upc.edu/record=b1432048~S1*cat
• Pattern recognition and machine learning - Bishop, C.M, Springer, 2006. ISBN: 0387310738
  http://cataleg.upc.edu/record=b1298151~S1*cat

Complementary:

• First look at rigorous probability theory - Rosenthal, J.S, World Scientific Publishing Company , 2006. ISBN: 978-9812703705
  http://cataleg.upc.edu/record=b1532807~S1*cat
• Graphical models, exponential families, and variational inference - Wainwright, M.J.; Jordan, M.I, Foundations and Trends in Machine Learning , .
  https://people.eecs.berkeley.edu/~wainwrig/Papers/WaiJor08_FTML.pdf

Web links

• You can find a pdf copy of MacKay's book http://www.inference.phy.cam.ac.uk/mackay/itila/

Previous capacities

Addendum

Contents

Teaching methodology

Evaluation methodology

Contingency plan