This work presents a sound probabilistic method for enforcing adherence of the marginal probabilities of a multi-label model to automatically discovered deterministic relationships among labels. In particular we focus on discovering two kinds of relationships among the labels. The first one concerns pairwise positive entailement: pairs of labels, where the presence of one implies the presence of the other in all instances of a dataset. The second concerns exclusion: sets of labels that do not coexist in the same instances of the dataset. These relationships are represented with a Bayesian network. Marginal probabilities are entered as soft evidence in the network and adjusted through probabilistic inference. Our approach offers robust improvements in mean average precision compared to the standard binary relavance approach across all 12 datasets involved in our experiments. The discovery process helps interesting implicit knowledge to emerge, which could be useful in itself.
A method for uncovering deterministic causal structures is introduced in @cite_9 . Similarly to our work, it aims at constructing a Bayesian network out of automatically discovered deterministic relationships. Important differences are that it does not consider latent variables, as in our representation of exclusions and our treatment of unaccounted causes of a label via leak nodes. It therefore requires relationships to be supported from the full dataset, which limits its practical usefulness, as rarely such relationships appear in real-world data.
@cite_9
2171533214
While standard procedures of causal reasoning as procedures analyzing causal Bayesian networks are custom-built for (non-deterministic) probabilistic structures, this paper introduces a Boolean procedure that uncovers deterministic causal structures. Contrary to existing Boolean methodologies, the procedure advanced here successfully analyzes structures of arbitrary complexity. It roughly involves three parts: first, deterministic dependencies are identified in the data; second, these dependencies are suitably minimalized in order to eliminate redundancies; and third, one or—in case of ambiguities—more than one causal structure is assigned to the minimalized deterministic dependencies.