Statistical Analysis of Networks and Systems

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

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: CB6, CTR5, CEE2.2, CG4,

Contents

1. Review of probability models
   Probability axioms, basic combinatorics, random variables, independence and conditional probability, Bayes formula, total probability. Expected values, variance-covariance matrix, inequalities (Markov, Chebyshev, Chernoff, Jensen), (weak) law large numbers, entropy and mutual information. Cross entropy as a cost function. Properties of Gaussian distributions, central limit theorem.
2. Estimation. Basic Machine Learning techniques for classification and regression
   Maximum likelihood and bayesian estimation. Decision functions, Loss, Risk, Empirical Risk minimization. Approximation and estimation. Bias-variance tradeoff. Classification. Linear regression. Basic neural networks architectures.
3. Linear models and dimensionality reduction
   Review of basic linear algebra results, spectral theorem for symmetric matrices, positive definite matrices, matrix calculus, trace operator, SVD, matrix norms, Eckart-Young theorem, condition number, dimensionality reduction, PCA, eigenfaces, Sparse representation, Fourier matrices, Graph signal processing

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
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991002876809706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Probability and statistics: the science of uncertainty - Evans, M.J.; Rosenthal, J.S, W.H. Freeman and Company, 2010. ISBN: 9781429224628
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991004003999706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• An introduction to probability theory and its applications - Feller, W, John Wiley and Sons, 1968. ISBN: 0471257117
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991000036749706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Pattern recognition and machine learning - Bishop, C.M, Springer, 2006. ISBN: 0387310738
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991003157379706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Linear Algebra and learning from data - G. Strang, Wellesley-Cambridge, 2020. ISBN: 978-06921963-8-0
  https://math.mit.edu/~gs/learningfromdata/
• An Introduction to Statistical Learning - G. James, D. Witten, T. Hastie, R. Tibshirani, Springer, 2021.
  https://www.statlearning.com/

Complementary:

• A first look at rigorous probability theory - Rosenthal, J.S, World Scientific , 2006. ISBN: 9812703713
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991004193689706711&context=L&vid=34CSUC_UPC:VU1&lang=ca

Previous capacities