On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition [PDF]
, 2010 This paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality.
AMMAR, Amine +2 more
core +6 more sources
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
semanticscholar +1 more source
Linear Hamilton Jacobi Bellman Equations in High Dimensions [PDF]
, 2014 The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than
Burdick, Joel W. +2 more
core +2 more sources
A geometric framework for modelling similarity search
, 1999 The aim of this paper is to propose a geometric framework for modelling similarity search in large and multidimensional data spaces of general nature, which seems to be flexible enough to address such issues as analysis of complexity, indexability, and ...
Pestov, Vladimir
core +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
semanticscholar +1 more source
A Reward Optimization Method Based on Action Subrewards in Hierarchical Reinforcement Learning
The Scientific World Journal, 2014 Reinforcement learning (RL) is one kind of interactive learning methods. Its main characteristics are “trial and error” and “related reward.” A hierarchical reinforcement learning method based on action subrewards is proposed to solve the problem of ...
Yuchen Fu +3 more
doaj +1 more source
Breaking the curse of dimensionality in nonparametric testing [PDF]
Journal of Econometrics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lavergne, Pascal, Patilea, Valentin
openaire +7 more sources
Taming the Curse of Dimensionality: Quantitative Economics with Deep Learning
Social Science Research NetworkWe argue that deep learning provides a promising approach to addressing the curse of dimensionality in quantitative economics. We begin by exploring the unique challenges involved in solving dynamic equilibrium models, particularly the feedback loop ...
Jesús Fernández-Villaverde +2 more
semanticscholar +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
semanticscholar +1 more source
High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality
Entropy, 2020 High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning.
Alexander N. Gorban +2 more
doaj +1 more source