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Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models
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Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Collection Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Organizer(s) Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Date(s) 15/06/2020 - 19/06/2020
linked URL https://www.cirm-math.com/cirm-virtual-event-2146.html
00:00:00 / 00:00:00
7 25

High-dimensional classification by sparse logistic regression

By Felix Abramovich

In this talk we consider high-dimensional classification. We discuss first high-dimensional binary classification by sparse logistic regression, propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic bounds for the resulting misclassification excess risk. Implementation of any complexity penalty-based criterion, however, requires a combinatorial search over all possible models. To find a model selection procedure computationally feasible for high-dimensional data, we consider logistic Lasso and Slope classifiers and show that they also achieve the optimal rate. We extend further the proposed approach to multiclass classification by sparse multinomial logistic regression.

This is joint work with Vadim Grinshtein and Tomer Levy.

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Citation data

  • DOI 10.24350/CIRM.V.19640203
  • Cite this video Abramovich, Felix (03/06/2020). High-dimensional classification by sparse logistic regression. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19640203
  • URL https://dx.doi.org/10.24350/CIRM.V.19640203

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Bibliography

  • ABRAMOVICH, Felix, GRINSHTEIN, Vadim, et LEVY, Tomer. Multiclass classification by sparse multinomial logistic regression. arXiv preprint arXiv:2003.01951, 2020. - https://arxiv.org/abs/2003.01951
  • ABRAMOVICH, Felix et GRINSHTEIN, Vadim. High-dimensional classification by sparse logistic regression. IEEE Transactions on Information Theory, 2018, vol. 65, no 5, p. 3068-3079. - https://doi.org/10.1109/TIT.2018.2884963
  • ALQUIER, Pierre, COTTET, Vincent, LECUÉ, Guillaume, et al. Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions. The Annals of Statistics, 2019, vol. 47, no 4, p. 2117-2144. - http://dx.doi.org/10.1214/18-AOS1742
  • BARTLETT, Peter L., JORDAN, Michael I., et MCAULIFFE, Jon D. Convexity, classification, and risk bounds. Journal of the American Statistical Association, 2006, vol. 101, no 473, p. 138-156. - https://www.jstor.org/stable/30047445
  • BELLEC, Pierre C., LECUÉ, Guillaume, TSYBAKOV, Alexandre B., et al. Slope meets lasso: improved oracle bounds and optimality. The Annals of Statistics, 2018, vol. 46, no 6B, p. 3603-3642. - http://dx.doi.org/10.1214/17-AOS1670
  • DANIELY, Amit, SABATO, Sivan, BEN-DAVID, Shai, et al. Multiclass learnability and the erm principle. The Journal of Machine Learning Research, 2015, vol. 16, no 1, p. 2377-2404. - http://jmlr.org/papers/volume16/daniely15a/daniely15a.pdf

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