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In a standard multi-output classification scenario, both features and labelsof training data are partially observed. This challenging issue is widelywitnessed due to sensor or database failures, crowd-sourcing and noisycommunication channels in industrial data analytic services. Classic methodsfor handling multi-output classification with incomplete supervisioninformation usually decompose the problem into an imputation stage thatreconstructs the missing training information, and a learning stage that buildsa classifier based on the imputed training set. These methods fail to fullyleverage the dependencies between features and labels. In order to take fulladvantage of these dependencies we consider a purely probabilistic setting inwhich the features imputation and multi-label classification problems arejointly solved. Indeed, we show that a simple Restricted Boltzmann Machine canbe trained with an adapted algorithm based on mean-field equations toefficiently solve problems of inductive and transductive learning in which bothfeatures and labels are missing at random. The effectiveness of the approach isdemonstrated empirically on various datasets, with particular focus on areal-world Internet-of-Things security dataset.

Robust Multi-Output Learning with Highly Incomplete Data via Restricted Boltzmann Machines