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CS8803-NS
Network Science
Fall 2013
Instructor: Constantine Dovrolis
[email protected]
http://www.cc.gatech.edu/~dovrolis/Courses/NetSci/
Disclaimers
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.
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 chisquared 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
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
Markov Chain Monte Carlo sampling –
Metropolis-Hasting algorithm
http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_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://upload.wikimedia.org/wikipedia/commons/5/5e/Metropolis_algorithm_convergence_example.png
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
http://paulbourke.net/miscellaneous/correlate/
Fisher transformation
http://en.wikipedia.org/wiki/File:Fisher_transformation.svg
P-value in one-sided hypothesis
tests
http://us.litroost.net/?p=889
Bootstraping
http://www-ssc.igpp.ucla.edu/personnel/russell/ESS265/Ch9/autoreg/node6.html
1-over-f noise (pink noise)
http://www.scholarpedia.org/article/1/f_noise