Digital medicine and the curse of dimensionality [PDF]
npj Digital Medicine, 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 ...
Visar Berisha +6 more
doaj +6 more sources
Fractional Norms and Quasinorms Do Not Help to Overcome the Curse of Dimensionality [PDF]
Entropy, 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 ...
Evgeny M. Mirkes +2 more
doaj +4 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. The approximation error of the neural network is $O(1/\sqrt{m})$ where $m$ is the size of networks, which overcomes the curse of dimensionality.
Yang, Yahong, Xiang, Yang
semanticscholar +6 more sources
Neural Mechanisms for Undoing the "Curse of Dimensionality". [PDF]
J Neurosci, 2015 Human behavior is marked by a sophisticated ability to attribute outcomes and events to choices and experiences with surprising nuance. Understanding the mechanisms that govern this ability is a major focus for cognitive neuroscience.
Vaidya AR.
europepmc +5 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 relu neural networks overcome the curse of dimensionality for partial integrodifferential equations [PDF]
Analysis and Applications, 2021 Deep neural networks (DNNs) with ReLU activation function are proved to be able to express viscosity solutions of linear partial integrodifferental equations (PIDEs) on state spaces of possibly high dimension $d$.
Lukas Gonon, C. Schwab
semanticscholar +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
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
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, 2019 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 +3 more
semanticscholar +5 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