Given a data set of N features, wherein some the features in this set were derived from other features from the same set, I am trying to discover inter dependencies between features (something like this Input feature(s) -> output feature(s)).
Note that,there can be multiple dependencies in the same feature set. Can someone suggest some technique to approach this problem.
For me it seems you are looking for Association Rule Learning. A quite simple example for an algorithm you could use is the Apriori Algorithm. You could try that one first and see if it does what you want to achieve. Then you can take a look into more sophisticated algorithms.
Generally these algorithms try to find associations between your features. E.g. they are able to find the implication, that many people who buy Coca Cola & Beer, will buy a pack of chips - if supported by the data:
$(Coca Cola, Beer)\implies(Chips)$.
Tree-based methods (e.g. random forests) and boosted tree methods (e.g. XGBoost) are usually quite good at detecting underlying relationships between features, and it's usually quite straightforward to extract measures of feature "importance".
You could try Principal Components Analysis, or a somewhat more informative alternative: least-squares feature selection.
