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Output Fisher Embedding Regression

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" (OFER) 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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Contributor : Telecomparis Hal <>
Submitted on : Friday, September 13, 2019 - 5:24:46 PM
Last modification on : Wednesday, June 24, 2020 - 4:19:54 PM


  • HAL Id : hal-02287837, version 1


Moussab Djerrab, A. Garcia Rojas, Maxime Sangnier, Florence d'Alché-Buc. Output Fisher Embedding Regression. Machine learning Journal, 2018, 108. ⟨hal-02287837⟩



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