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