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.
Table of Contents
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
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