Curse of dimensionality refers to the problem that the space of possible sets of parameter values grows exponentially with the number of unknown parameters, severely impairing the search for the globally optimal parameter values. From: Computational Systems Biology, 2006 ...
Curse of dimensionalityDifferential privacyIn general, just suppressing identifiers from released micro-data is insufficient for privacy protection. It has been shown that the risk of re-identification increases with the dimensionality of the released records. Hence, sound anonymization procedures are ...
This paper considers how the large number of features in vast digital health data can challenge the development of robust AI models—a phenomenon known as “the curse of dimensionality” in statistical learning theory. We provide an overview of the curse of dimensionality in the context of ...
Partial Differential Equations and Applications (2023) 4:27 https://doi.org/10.1007/s42985-023-00240-4 ORIGINAL PAPER Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus Akihiko Takahashi1 · Toshihiro Yamada2,3 Received: 22 ...
This work is aimed at reducing the dimensionality in the spectral stochastic finite element method (SSFEM)–thus the computational cost–through a domain decomposition (DD) method. This reduction hinges on some new mathematical results on domain size dependence of the Karhunen–Loève (KL) expansion...
This isn’t a defect of the tidyverse, it’s the result of an architectural decision on the part of the original language designers; it probably seemed like a good idea at the time. The tidyverse functions are just doing the best they can with the existing architecture. ...
We propose a decomposition procedure to deflate the dimensionality problem by splitting it into manageable pieces and coordinating their solution. There are two main computational advantages in the use of decomposition methods. First, the subproblems are, by definition, smaller than the original problem...
Extracting a large number of significant features increases the representative power of the feature vector and improves the query precision. However, each feature is a dimension in the representation space, consequently handling more features worsen the dimensionality curse. The problem derives from the ...
The numerical approximation of parametric partial differential equations D(u,y)=0 is a computational challenge when the dimension d of the parameter vector y is large, due to the so-called curse of dimensionality. It was recently shown in [1], [2] that, for a certain class of elliptic PD...
The paper shows that the dynamic programming (DP) method due to Bellman, when augmented with an optimum sensitivity analysis, provides a mathematical basis for the above decomposition and overcomes the curse of dimensionality that limited the original formulation of DP. Numerical examples are cited....