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• W3201520726 abstract "Remi FlamaryLaboratoire Lagrange, Observatoire de la Cote d’Azur, Universite de NiceSophia-AntipolisAlain RakotomamonjyLITIS, Universite de RouenGilles GassoLITIS, INSA de Rouen5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.2 Similarity Based Multi-Task Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.2.1 Multi-Task Learning Framework . . . . . . . . . . . . . . . . . . . . . . . . 1065.2.2 Similarity-Based Regularization . . . . . . . . . . . . . . . . . . . . . . . . . 1075.2.3 Solving the Multi-Task Learning Problem . . . . . . . . . . . . . . 1085.3 Non-Convex Proximal Algorithm for Learning Similarities . . . . . 1105.3.1 Bilevel Optimization Framework . . . . . . . . . . . . . . . . . . . . . . . . 1105.3.2 Gradient Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.3.3 Constraints on P and λt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.3.4 Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.4 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.4.1 Toy Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.4.2 Real-World Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.4.2.1 Experimental Set-Up . . . . . . . . . . . . . . . . . . . . . . . 1195.4.2.2 School Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.4.2.3 Brain Computer Interface Dataset . . . . . . . . 1215.4.2.4 OCR Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127VectorThis chapter addresses the problem of learning constrained task relatedness in a graph-regularized multi-task learning framework. In such a context,the weighted adjacency matrix of a graph encodes the knowledge on tasksimilarities and each entry of this matrix can be interpreted as a hyperparameter of the learning problem. This task relation matrix is learned via abilevel optimization procedure where the outer level optimizes a proxy of thegeneralization errors over all tasks with respect to the similarity matrix andthe inner level estimates the parameters of the tasks knowing this similaritymatrix. Constraints on task similarities are also taken into account in thisoptimization framework and they allow the task similarity matrix to be moreinterpretable, for instance, by imposing a sparse similarity matrix. Since theglobal problem is non-convex, we propose a non-convex proximal algorithmthat provably converges to a stationary point of the problem. Empirical evidence illustrates the approach is competitive compared to existing methodsthat also learn task relation and exhibits an enhanced interpretability of thelearned task similarity matrix." @default.
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• W3201520726 date "2014-10-23" @default.
• W3201520726 modified "2023-10-16" @default.
• W3201520726 title "Learning Constrained Task Similarities in Graph-Regularized Multi-Task Learning" @default.
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• W3201520726 doi "https://doi.org/10.1201/b17558-8" @default.
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