High-dimentional classification with deep neural networks: decision boundaries, noise, and margin | Vidéo | Carmin.tv

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High-dimentional classification with deep neural networks: decision boundaries, noise, and margin

By Philipp Petersen

Appears in collection : SIGMA (Signal, Image, Geometry, Modeling, Approximation) / SIGMA (Signal, Image, Géométrie, Modélisation, Approximation)

we discuss classification problems in high dimension. We study classification problems using three classical notions: complexity of decision boundary, noise, and margin. We demonstrate that under suitable conditions on the decision boundary, classification problems can be very efficiently approximated, even in high dimensions. If a margin condition is assumed, then arbitrary fast approximation rates can be achieved, despite the problem being high-dimensional and discontinuous. We extend the approximation results ta learning results and show close ta optimal learning rates for empirical risk minimization in high dimensional classification.

Information about the video

Date of recording 29/10/2024
Date of publication 22/11/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20257603
Cite this video Petersen, Philipp (29/10/2024). High-dimentional classification with deep neural networks: decision boundaries, noise, and margin. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20257603
URL https://dx.doi.org/10.24350/CIRM.V.20257603

Domain(s)

Bibliography

PETERSEN, Philipp et VOIGTLAENDER, Felix. Optimal approximation of piecewise smooth functions using deep ReLU neural networks. Neural Networks, 2018, vol. 108, p. 296-330. - https://doi.org/10.1016/j.neunet.2018.08.019
CARAGEA, Andrei, PETERSEN, Philipp, et VOIGTLAENDER, Felix. Neural network approximation and estimation of classifiers with classification boundary in a Barron class. The Annals of Applied Probability, 2023, vol. 33, no 4, p. 3039-3079. - https://doi.org/10.1214/22-AAP1884
KIM, Yongdai, OHN, Ilsang, et KIM, Dongha. Fast convergence rates of deep neural networks for classification. Neural Networks, 2021, vol. 138, p. 179-197. - https://doi.org/10.1016/j.neunet.2021.02.012
IMAIZUMI, Masaaki et FUKUMIZU, Kenji. Deep neural networks learn non-smooth functions effectively. In : The 22nd international conference on artificial intelligence and statistics. PMLR, 2019. p. 869-878. - https://proceedings.mlr.press/v89/imaizumi19a.html
LERMA-PINEDA, Andres Felipe, PETERSEN, Philipp, FRIEDER, Simon, et al. Dimension-independent learning rates for high-dimensional classification problems. arXiv preprint arXiv:2409.17991, 2024. - https://doi.org/10.48550/arXiv.2409.17991
GARCIA J., PETERSEN P., Classification problem with Barron regular boundaries and margin condition, ta appear 2024 -

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