On the robustness of the generalized fused lasso to prior specifications
| Autor: | Franck Picard, Holger Hoefling, Vivian Viallon, Sophie Lambert-Lacroix |
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| Přispěvatelé: | Unité Mixte de Recherche Epidémiologique et de Surveillance Transport Travail Environnement (UMRESTTE UMR T9405), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), Biologie Computationnelle et Mathématique (TIMC-IMAG-BCM), Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525 (TIMC-IMAG), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Novartis Pharma AG, Statistique en grande dimension pour la génomique, Département PEGASE [LBBE] (PEGASE), Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2014 |
| Předmět: |
0301 basic medicine
Statistics and Probability Generalized linear model MODELE STATISTIQUE INTELLIGENCE ARTIFICIELLE Machine learning computer.software_genre 01 natural sciences Oracle Theoretical Computer Science 010104 statistics & probability 03 medical and health sciences [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Robustness (computer science) 0101 mathematics Prior information Mathematics Forgetting business.industry Model selection MODELISATION ComputingMethodologies_PATTERNRECOGNITION 030104 developmental biology Computational Theory and Mathematics MODELE LINEAIRE Artificial intelligence Statistics Probability and Uncertainty business computer Algorithm Sparse regression |
| Zdroj: | Statistics and Computing Statistics and Computing, Springer Verlag (Germany), 2016, 26 (1), pp.285-301. ⟨10.1007/s11222-014-9497-6⟩ Statistics and Computing, 2016, 26 (1), pp.285-301. ⟨10.1007/s11222-014-9497-6⟩ |
| ISSN: | 1573-1375 0960-3174 |
| DOI: | 10.1007/s11222-014-9497-6 |
| Popis: | Using networks as prior knowledge to guide model selection is a way to reach structured sparsity. In particular, the fused lasso that was originally designed to penalize differences of coefficients corresponding to successive features has been generalized to handle features whose effects are structured according to a given network. As any prior information, the network provided in the penalty may contain misleading edges that connect coefficients whose difference is not zero, and the extent to which the performance of the method depend on the suitability of the graph has never been clearly assessed. In this work we investigate the theoretical and empirical properties of the adaptive generalized fused lasso in the context of generalized linear models. In the fixed $$p$$p setting, we show that, asymptotically, adding misleading edges in the graph does not prevent the adaptive generalized fused lasso from enjoying asymptotic oracle properties, while forgetting suitable edges can be more problematic. These theoretical results are complemented by an extensive simulation study that assesses the robustness of the adaptive generalized fused lasso against misspecification of the network as well as its applicability when theoretical coefficients are not exactly equal. Our contribution is also to evaluate the applicability of the generalized fused lasso for the joint modeling of multiple sparse regression functions. Illustrations are provided on two real data examples. |
| Databáze: | OpenAIRE |
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