Learning with a Fisher surrogate loss in a small data regime

We introduce a novel framework, Output Fisher Embedding Regression (OFER), that uses a Fisher vector representation of output data and provides prediction by solving an appropriate pre-image problem. OFER takes advantage of the implicit structure of the marginal probability distribution of the output to improve performance in prediction. Although the proposed approach is general and versatile, we put a stress on the Gaussian mixture model for modelling the output data and design a closed-form solution for the corresponding pre-image problem. Numerical results on a drug activity prediction task and a semantic multi-class classification show the relevance of the approach in small data regime.