Probabilistic attribute correspondences

Probabilistic attribute correspondences extend attribute correspondences by generating multiple possible models, modeling uncertainty about which one is correct by using probability theory. Such probabilities can then be combined to represent possible schema mappings, based on which query processing can be performed. 

Probabilistic attribute correspondences can state that R.Cardlnfo.cardNum matches S.Cardlnformation.cardNum with a probability of 0.7 and S.HotelCard-Information.clientNum with a probability of 0.3. 

The model of probabilistic attribute correspondences is based on the model of probabilistic schema mapping [Dong et al. 2007], extending the concept of schema... 

A probabilistic attribute correspondence (A, Aj, p) is any attribute correspondence in a probabilistic schema mapping. 

We can create the probability that is assigned with an attribute correspondence (Ai,Aj) by summing all probabilities of schema matchings in which (A, Aj) appears. That is, for a probabilistic attribute correspondence (A, Aj, p) we compute p to be ... 

The first observation is that top-AT schema matchings play a pivotal role in identifying attribute correspondences. We have shown that top-AT matchings can serve in identifying both good candidates for contextual attribute correspondences and probabilistic attribute correspondences. In this research direction, there are still many open questions, first of which is the ability to identify top-AT matchings in polynomial time. 

A model was proposed in Magnani et al. [2005] for combining semantic and probabilistic attribute correspondences using constructs of uncertain semantic relationships in an ER model. An uncertain semantic relationship is a distribution of beliefs over the set of all possible semantic relationships, using belief functions [Shafer 1976], The set of possible semantic relations serve as the frame of discernment (marked ), based on which two functions are defined, namely belief and plausability. Both functions assign a value to a subset of the frame of discernment, starting from the basic probability mass that is assigned with each element in the frame of discernment. Belief of a set A e sums the probability mass of all subsets B c A. Plausability of a set A is the sum of all subsets that intersect with A, i.e., all B such that A n B 0. 

Contextual and by-tuple probabilistic attribute correspondences seem to be complementary. A by-tuple probabilistic attribute correspondence represents a situation in which there is uncertainty as to whether a given tuple should be interpreted using one correspondence or the other. Contextual attribute correspondences models exactly such knowledge. Therefore, By-tuple probabilistic attribute correspondence is needed whenever no information regarding the contextual attribute correspondence is available. Whenever contextual attribute correspondence is gathered automatically, using statistical methods as described in Sect. 3.2, another layer of uncertainty is added to the modeling. Therefore, contextual attribute correspondences should also be extended to provide probabilistic alternative versions. 

Expressive power A natural question to ask at this point is whether probabilistic mediated schemas provide any added expressive power compared to deterministic ones. Theorem 8 shows that if we consider one-to-many schema mappings, where one source attribute can be mapped to multiple mediated attributes, then any combination of a p-med-schema and p-mappings can be equivalently represented using a deterministic mediated schema with p-mappings, but may not be represented using a p-med-schema with deterministic schema mappings. Note that we can easily extend the definition of query answers to one-to-many mappings, as one mediated attribute can correspond to no more than one source attribute. 

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