How to specify important attributes? Assume a set of loosely structured data (e.g. Web tables/Linked Open Data), composed of many data sources. There is no common schema followed by the data and each source can use synonym attributes to describe the values (e.g. "nationality" vs "bornIn"). 

My goal is to find some "important" attributes that somehow "define" the entities that they describe. So, when I find the same value for such an attribute, I will know that the two descriptions are most likely about the same entity (e.g. the same person).

For example, the attribute "lastName" is more discriminative than the attribute "nationality". 

How could I (statistically) find such attributes that are more important than others?

A naive solution would be to take the average IDF of the values of each attribute and make this the "importance" factor of the attribute. A similar approach would be to count how many distinct values appear for each attribute.

I have seen the term feature, or attribute selection in machine learning, but I don't want to discard the remaining attributes, I just want to put higher weights to the most important ones.
A possible solution is to calculate the information gain associated to each attribute:
$$I_{E}(f) = - \sum \limits_{i = 1}^m f_ilog_2f_i$$
Initially you have the whole dataset, and compute the information gain of each item. The item with the best information gain is the one you should use to partition the dataset (considering the item's values). Then, perform the same computations for each item (but the ones selected), and always choose the one which best describes/differentiates the entries from your dataset.
There are implementations available for such computations. Decision trees usually base their feature selection on the features with best information gain. You may use the resulting tree structure to find these important items.