  Causal variables in Markov boundary (MB) have been widely applied in
extensive single-label tasks. While few researches focus on the causal variable
discovery in multi-label data due to the complex causal relationships. Since
some variables in multi-label scenario might contain causal information about
multiple labels, this paper investigates the problem of multi-label causal
variable discovery as well as the distinguishing between common causal
variables shared by multiple labels and label-specific causal variables
associated with some single labels. Considering the multiple MBs under the
non-positive joint probability distribution, we explore the relationships
between common causal variables and equivalent information phenomenon, and find
that the solutions are influenced by equivalent information following different
mechanisms with or without existence of label causality. Analyzing these
mechanisms, we provide the theoretical property of common causal variables,
based on which the discovery and distinguishing algorithm is designed to
identify these two types of variables. Similar to single-label problem, causal
variables for multiple labels also have extensive application prospects. To
demonstrate this, we apply the proposed causal mechanism to multi-label feature
selection and present an interpretable algorithm, which is proved to achieve
the minimal redundancy and the maximum relevance. Extensive experiments
demonstrate the efficacy of these contributions.
