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Introduction to Network Science: Key Problems, Theories, and Statistical Methods

This course, led by Professor Constantine Dovrolis at Georgia Tech, delves into Network Science and its statistical foundations. Students will explore critical problems such as sampling from large networks, traceroute bias, and temporal correlation inference. The curriculum includes hypothesis testing, stochastic graph models, and techniques like Maximum Likelihood Estimation and Markov-Chain-Monte-Carlo (MCMC) sampling. Real-world applications and advanced coupling metrics will also be discussed, equipping students with the necessary tools to analyze and predict network behaviors.

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Introduction to Network Science: Key Problems, Theories, and Statistical Methods

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  1. CS8803-NSNetwork ScienceFall 2013 Instructor: Constantine Dovrolis constantine@gatech.edu http://www.cc.gatech.edu/~dovrolis/Courses/NetSci/

  2. Disclaimers The following slides include only the figures or videos that we use in class; they do not include detailed explanations, derivations or descriptionscovered in class. Many of the following figures are copied from open sources at the Web. I do not claim any intellectual property for the following material.

  3. Outline • Network science and statistics • Four important problems: • Sampling from large networks • Sampling bias in traceroute-like probing • Network inference based on temporal correlations • Prediction of missing & spurious links

  4. Also learn about: • Traceroute-like network discovery • A couple of nice examples of constructing hypothesis tests • One of them is based on an interesting Chernoff bound • The other is based on the Pearson chi-squared goodness of fit test

  5. Also learn about: • Stochastic graph models and how to fit them to data in Bayesian framework • Maximum-Likelihood-Estimation • Markov-Chain-Monte-Carlo (MCMC) sampling • Metropolis-Hastings rule • Area-Under-Curve (ROC) evaluation of a classifier

  6. Appendix – some background

  7. ROC and Area-Under-Curve http://gim.unmc.edu/dxtests/roc3.htm http://www.intechopen.com/books/data-mining-applications-in-engineering-and-medicine/examples-of-the-use-of-data-mining-methods-in-animal-breeding

  8. Markov Chain Monte Carlo sampling – Metropolis-Hasting algorithm The result of three Markov chains running on the 3D Rosenbrock function using the Metropolis-Hastings algorithm. The algorithm samples from regions where the posterior probability is high and the chains begin to mix in these regions. The approximate position of the maximum has been illuminated. Note that the red points are the ones that remain after the burn-in process. The earlier ones have been discarded. http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm http://upload.wikimedia.org/wikipedia/commons/5/5e/Metropolis_algorithm_convergence_example.png

  9. Also learn about: • More advanced coupling metrics (than Pearson’s cross-correlation) • Coherence, synchronization likelihood, wavelet coherence, Granger causality, directed transfer function, and others • Bootstrap to calculate a p-value • And frequency-domain bootstrap for timeseries • The Fisher transformation • A result from Extreme Value Theory • Multiple Testing Problem • False Discovery Rate (FDR) • The linear step-up FDR control method • Pink noise

  10. Appendix – some background

  11. http://paulbourke.net/miscellaneous/correlate/

  12. Fisher transformation http://en.wikipedia.org/wiki/File:Fisher_transformation.svg

  13. P-value in one-sided hypothesis tests http://us.litroost.net/?p=889

  14. Bootstraping http://www-ssc.igpp.ucla.edu/personnel/russell/ESS265/Ch9/autoreg/node6.html

  15. 1-over-f noise (pink noise) http://www.scholarpedia.org/article/1/f_noise

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