Nonlinear Functional Output Regression: a Dictionary Approach

In many fields, each data instance consists in a high number of measurements of the same underlying phenomenon. Such high dimensional data generally enjoys strong smoothness across features which can be exploited through functional modelling. In the setting of functional output regression, we introduce projection learning, a novel dictionary-based approach combining a representation of the output in a dictionary with the minimization of a functional loss. This general method is instantiated with square loss and reproducing kernel Hilbert spaces of vector-valued functions, allowing to impose some structure on the model. The resulting algorithm is backed theoretically with an excess risk bound leading to consistency, while experiments on several datasets show that it is competitive compared to other nonlinear approaches at a low computational cost. In addition, the method is shown to be versatile as it can deal with sparsely sampled functions and can be used with various dictionaries.