Digital medicine and the curse of dimensionality. [PDF]
NPJ Digit Med, 2021 Digital health data are multimodal and high-dimensional. A patient’s health state can be characterized by a multitude of signals including medical imaging, clinical variables, genome sequencing, conversations between clinicians and patients, and ...
Berisha V +6 more
europepmc +2 more sources
Resolution of the curse of dimensionality in single-cell RNA sequencing data analysis. [PDF]
Life Sci Alliance, 2022 This work formulates a noise reduction method, RECODE, which resolves the curse of dimensionality in noisy high-dimensional data, including scRNA-seq data, for effective downstream analyses.
Imoto Y +9 more
europepmc +2 more sources
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs [PDF]
Trans. Mach. Learn. Res., 2023 Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing.
Ke Chen, Chunmei Wang, Haizhao Yang
openalex +3 more sources
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations [PDF]
SN Partial Differential Equations and Applications, 2020 Deep neural networks and other deep learning methods have very successfully been applied to the numerical approximation of high-dimensional nonlinear parabolic partial differential equations (PDEs), which are widely used in finance, engineering, and ...
Martin Hutzenthaler +7 more
semanticscholar +5 more sources
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations. [PDF]
SN Partial Differ Equ Appl, 2020 Recently, so-called full-history recursive multilevel Picard (MLP) approximation schemes have been introduced and shown to overcome the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations (PDEs ...
Beck C, Gonon L, Jentzen A.
europepmc +3 more sources
Gene Expression-Based Cancer Classification for Handling the Class Imbalance Problem and Curse of Dimensionality. [PDF]
Int J Mol SciCancer is a leading cause of death globally. The majority of cancer cases are only diagnosed in the late stages of cancer due to the use of conventional methods. This reduces the chance of survival for cancer patients.
Al-Azani S +3 more
europepmc +2 more sources
Fractional Norms and Quasinorms Do Not Help to Overcome the Curse of Dimensionality. [PDF]
Entropy (Basel), 2020 The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using the Manhattan distance and even fractional lp quasinorms (for p less than 1) can help to overcome the curse of ...
Mirkes EM, Allohibi J, Gorban A.
europepmc +3 more sources
Addressing the curse of dimensionality in stochastic dynamics: a Wiener path integral variational formulation with free boundaries. [PDF]
Proc Math Phys Eng Sci, 2020 A Wiener path integral variational formulation with free boundaries is developed for determining the stochastic response of high-dimensional nonlinear dynamical systems in a computationally efficient manner.
Petromichelakis I, Kougioumtzoglou IA.
europepmc +2 more sources
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. [PDF]
Proc Math Phys Eng Sci, 2020 For a long time it has been well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows polynomially both in the dimension and in the ...
Hutzenthaler M +4 more
europepmc +3 more sources
Approximation of Functionals by Neural Network without Curse of Dimensionality [PDF]
Journal of Machine Learning, 2022 In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces.
Yahong Yang, Yang Xiang
semanticscholar +1 more source