Since the coefficient is between 0 and 1, I would like to know if the MIC allows us to know if the relationship between the two variables are positive or negative ?
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No, it does not. 0 implies statistically independent variables and 1 perfect (noiseless) functional relationship, up to the approximation determined by the parameter $\alpha$ which controls the grid size.
It is difficult to define positive and negative relationship. You can only do it if the relationship is monotone. If you are just interested in monotonic relationships between variables I would suggest to use the Spearman's rank coefficient: this is equal to 1 when $Y$ increases at the increase of $X$ and it is equal to -1 when $Y$ decreases at the increase of $X$.
There are other interesting statistics proposed by MIC's authors. See the supplementary material of the Science paper here.
- MAS: which measures the deviation from monotonicity
- MEV: which measures if the relationship is functional (similar to MIC but only 2 bins for either $X$ or $Y$ are used, probably this approach would interfere with equitability)
- MCN: which measures the complexity of the relationships (basically the number of cells used)
In your case, it would be interesting to compare the top ranked relationships according to Spearman's rank (either positive or negative), to MIC, and to MAS.
