Correlation
Correlations between many elements in a system inevitably contain indirect correlations from other elements.
You should also be very careful when you calculate a correlation between Time series.
Topics
Handling indirect correlation
The indirect correlation leads us to inaccurate prediction. There are several ways to filter out those indirect edges with spurious correlation:
 Correlation of correlations
 Partial correlation
 Mutual information based approach (citation needed).
 Methods for the Inverse Ising problem
 network deconvolution: http://www.nature.com/nbt/journal/v31/n8/abs/nbt.2635.html
 Network link prediction by global silencing of indirect correlations
Aggregating correlation
Sometimes, we want to average correlation values. A standard method is performing Fisher transformation and average the z values then transform it back to correlation coefficient.
Constructing networks from correlation matrices
Correlation Matrix
Correlation and causation
Generalized ways of inferring associations
 Reshef et al. Detecting Novel Associations in Large Data Sets
 Kinney and Atwal, Equitability, mutual information, and the maximal information coefficient
Articles
 http://www.johndcook.com/blog/2008/11/05/howtocalculatepearsoncorrelationaccurately/  don’t expect that the small difference between two large numbers will be accurate.
 Cosine similarity, Pearson correlation, and OLS coefficients
References
 http://en.wikipedia.org/wiki/Partial correlation
 Graphical interaction models for multivariate time series by Rainer Dahlhaus
 Comparing association network algorithms for reverse engineering of largescale gene regulatory networks: synthetic versus real data

PLoS biology: LargeScale Mapping and Validation of Escherichia coli Transcriptional Regulation from a Compendium of Expression Profiles  Mutual information based method