CS8803-NS Network Science Fall 2013 Instructor: Constantine Dovrolis

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CS8803-NS Network Science Fall 2013

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Presentation transcript:

CS8803-NS Network Science Fall 2013 Instructor: Constantine Dovrolis

The following slides include only the figures or videos that we use in class; they do not include detailed explanations, derivations or descriptions covered 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. Disclaimers

Outline Network science and statistics Four important problems: 1.Sampling from large networks 2.Sampling bias in traceroute-like probing 3.Network inference based on temporal correlations 4.Prediction of missing & spurious links

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

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

Appendix – some background

ROC and Area-Under-Curve

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.Markov chainsRosenbrock functionposterior probability

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

Appendix – some background

Fisher transformation

P-value in one-sided hypothesis tests

Bootstraping

1-over-f noise (pink noise)