Output Fisher embedding regression

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Abstract

We investigate the use of Fisher vector representations in the output space in the context of structured and multiple output prediction. A novel, general and versatile method called output Fisher embedding regression is introduced. Based on a probabilistic modeling of training output data and the minimization of a Fisher loss, it requires to solve a pre-image problem in the prediction phase. For Gaussian Mixture Models and State-Space Models, we show that the pre-image problem enjoys a closed-form solution with an appropriate choice of the embedding. Numerical experiments on a wide variety of tasks (time series prediction, multi-output regression and multi-class classification) highlight the relevance of the approach for learning under limited supervision like learning with a handful of data per label and weakly supervised learning.

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Djerrab, M., Garcia, A., Sangnier, M., & d’Alché-Buc, F. (2018). Output Fisher embedding regression. Machine Learning, 107(8–10), 1229–1256. https://doi.org/10.1007/s10994-018-5698-0

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