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Additive models form a widely popular class of regression models whichrepresent the relation between covariates and response variables as the sum oflow-dimensional transfer functions. Besides flexibility and accuracy, a keybenefit of these models is their interpretability: the transfer functionsprovide visual means for inspecting the models and identifying domain-specificrelations between inputs and outputs. However, in large-scale problemsinvolving the prediction of many related tasks, learning independently additivemodels results in a loss of model interpretability, and can cause overfittingwhen training data is scarce. We introduce a novel multi-task learning approachwhich provides a corpus of accurate and interpretable additive models for alarge number of related forecasting tasks. Our key idea is to share transferfunctions across models in order to reduce the model complexity and ease theexploration of the corpus. We establish a connection with sparse dictionarylearning and propose a new efficient fitting algorithm which alternates betweensparse coding and transfer function updates. The former step is solved via anextension of Orthogonal Matching Pursuit, whose properties are analyzed using anovel recovery condition which extends existing results in the literature. Thelatter step is addressed using a traditional dictionary update rule.Experiments on real-world data demonstrate that our approach compares favorablyto baseline methods while yielding an interpretable corpus of models, revealingstructure among the individual tasks and being more robust when training datais scarce. Our framework therefore extends the well-known benefits of additivemodels to common regression settings possibly involving thousands of tasks.

Multi-task additive models with shared transfer functions based on dictionary learning