A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations [PDF]
Memoirs of the American Mathematical Society, 2018 Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and ...
P. Grohs +3 more
semanticscholar +1 more source
Burning Sage: Reversing the Curse of Dimensionality in the Visualization of High-Dimensional Data [PDF]
Journal of Computational And Graphical Statistics, 2020 In high-dimensional data analysis, the curse of dimensionality reasons that points tend to be far away from the center of the distribution and on the edge of high-dimensional space.
U. Laa, D. Cook, Stuart Lee
semanticscholar +1 more source
On deep learning as a remedy for the curse of dimensionality in nonparametric regression
Annals of Statistics, 2019 Assuming that a smoothness condition and a suitable restriction on the structure of the regression function hold, it is shown that least squares estimates based on multilayer feedforward neural networks are able to circumvent the curse of dimensionality ...
B. Bauer, M. Kohler
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Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review [PDF]
International Journal of Automation and Computing, 2016 The paper reviews and extends an emerging body of theoretical results on deep learning including the conditions under which it can be exponentially better than shallow learning.
T. Poggio +4 more
semanticscholar +1 more source
Artificial Intelligence ReviewElectroencephalography (EEG) is commonly employed to diagnose and monitor brain disorders, however, manual analysis is time-consuming. Hence, researchers nowadays are increasingly leveraging artificial intelligence (AI) techniques for automatic analysis ...
Arti Anuragi +2 more
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Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems [PDF]
Analysis and Applications, 2019 In this paper, we establish that for a wide class of controlled stochastic differential equations (SDEs) with stiff coefficients, the value functions of corresponding zero-sum games can be represented by a deep artificial neural network (DNN), whose ...
C. Reisinger, Yufei Zhang
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A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients [PDF]
Communications in Mathematical Sciences, 2018 In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, object and face recognition, natural language processing, fraud detection ...
Arnulf Jentzen +2 more
semanticscholar +1 more source
Advanced Materials, EarlyView.This article summarizes significant technological advancements in materials, photonic devices, and bio‐interfaced systems, which demonstrate successful applications for impacting human healthcare via improved therapies, advanced diagnostics, and on‐skin health monitoring.
Seunghyeb Ban +5 more
wiley +1 more source
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks [PDF]
Electronic Journal of Probability, 2019 Parabolic partial differential equations (PDEs) are widely used in the mathematical modeling of natural phenomena and man made complex systems. In particular, parabolic PDEs are a fundamental tool to determine fair prices of financial derivatives in the ...
Martin Hutzenthaler +2 more
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Advanced Science, EarlyView.A high‐resolution micro‐electrocorticographic (µECoG) brain‐computer interface (BCI) for real‐time motor decoding is reported. The application of flexible, scalable µECoG electrode arrays overcomes the insufficient spatial resolution in conventional ECoG BCIs.
Erda Zhou +15 more
wiley +1 more source