Before revision:  We propose an information-based criterion that identifies couplings that are either weak , or statistically unsupported . We show that our procedure allows one to remove more than 90 \% of the PM couplings, while preserving the predictive and generative properties of the original dense PM.
After revision:  We propose an information-based criterion that identifies couplings that are either weak , or statistically unsupported couplings. For several protein families, our procedure allows one to remove more than 90 \% of the PM couplings, while preserving the predictive and generative properties of the original dense PM.