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Classifier chains are popular and effective method to tackle a multi-labelclassification problem. The aim of this paper is to study the asymptoticproperties of the chain model in which the conditional probabilities are of thelogistic form. In particular we find conditions on the number of labels and thedistribution of feature vector under which the estimated mode of the jointdistribution of labels converges to the true mode. Best of our knowledge, thisimportant issue has not yet been studied in the context of multi-labellearning. We also investigate how the order of model building in a chaininfluences the estimation of the joint distribution of labels. We establish thelink between the problem of incorrect ordering in the chain and incorrect modelspecification. We propose a procedure of determining the optimal ordering oflabels in the chain, which is based on using measures of correct specificationand allows to find the ordering such that the consecutive logistic models arebest possibly specified. The other important question raised in this paper ishow accurately can we estimate the joint posterior probability when theordering of labels is wrong or the logistic models in the chain are incorrectlyspecified. The numerical experiments illustrate the theoretical results.

Asymptotic consistency and order specification for logistic classifier chains in multi-label learning