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The task is to learn a classifier to predict the individual labels of future individual instances. Prior work on LLP for multi-class data has yet to develop a theoretically grounded algorithm. In this work, we provide a theoretically grounded approach to LLP based on a reduction to learning with label noise, using the forward correction (FC) loss of \\citet{Patrini2017MakingDN}. We establish an excess risk bound and generalization error analysis for our approach, while also extending the theory of the FC loss which may be of independent interest. 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