Concentration inequalities for non-causal random fields

Garnier, Rémy; Langhendries, Raphaël

doi:10.1214/22-ejs1992

Cited by 2 publications

(3 citation statements)

References 25 publications

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“…Notice that the infimum is always attained. The following is the main result of this section; it tells us that τ L L is indeed the optimal stopping time for problem (11). It comes from [36, Theorem 1.2].…”

Section: Optimal Number Of Layersmentioning

confidence: 96%

“…Our first goal is to give concentration inequalities for the outputs of the hidden layers of a generic SDNN. This problem has already been studied for particular types of SDNNs in [11], [34]. In the former, the authors establish a framework for modeling non-causal random fields and prove a Hoeffding-type concentration inequality; it is especially important because it can be applied to the field of Natural Language Processing (NLP).…”

Section: B Contributionsmentioning

confidence: 99%

“…, L }. Then, (i) the stopping time τ L L is optimal for (11); (ii) if τ ⋆ is any optimal stopping time for (11), then τ L L ≤ τ ⋆ P (X,Y )∼D -a.s.…”

Section: Optimal Number Of Layersmentioning

confidence: 99%

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Concentration Inequalities and Optimal Number of Layers for Stochastic Deep Neural Networks

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2023

IEEE Access

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We state concentration inequalities for the output of the hidden layers of a stochastic deep neural network (SDNN), as well as for the output of the whole SDNN. These results allow us to introduce an expected classifier (EC), and to give probabilistic upper bound for the classification error of the EC. We also state the optimal number of layers for the SDNN via an optimal stopping procedure. We apply our analysis to a stochastic version of a feedforward neural network with ReLU activation function.

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Section: Optimal Number Of Layersmentioning

confidence: 96%

Section: B Contributionsmentioning

confidence: 99%

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Concentration Inequalities and Optimal Number of Layers for Stochastic Deep Neural Networks

Caprio

Mukherjee

2023

IEEE Access

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A Survey of Deep Learning for Alzheimer’s Disease

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Wang

et al. 2023

MAKE

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Alzheimer’s and related diseases are significant health issues of this era. The interdisciplinary use of deep learning in this field has shown great promise and gathered considerable interest. This paper surveys deep learning literature related to Alzheimer’s disease, mild cognitive impairment, and related diseases from 2010 to early 2023. We identify the major types of unsupervised, supervised, and semi-supervised methods developed for various tasks in this field, including the most recent developments, such as the application of recurrent neural networks, graph-neural networks, and generative models. We also provide a summary of data sources, data processing, training protocols, and evaluation methods as a guide for future deep learning research into Alzheimer’s disease. Although deep learning has shown promising performance across various studies and tasks, it is limited by interpretation and generalization challenges. The survey also provides a brief insight into these challenges and the possible pathways for future studies.

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Concentration inequalities for non-causal random fields

Cited by 2 publications

References 25 publications

Concentration Inequalities and Optimal Number of Layers for Stochastic Deep Neural Networks

Concentration Inequalities and Optimal Number of Layers for Stochastic Deep Neural Networks

A Survey of Deep Learning for Alzheimer’s Disease

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