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 …

Various tools can be used to calculate or estimate the dimension of measures. Using a
probabilistic interpretation, we propose very simple proofs for the main inequalities related to …

Properties of data distributions can be assessed at both global and local scales. At a highly
localized scale, a fundamental measure is the local intrinsic dimensionality (LID), which …

It is widely believed in the pattern recognition field that when a fixed number of training
samples is used to design a classifier, the generalization error of the classifier tends to …

High-dimensional data are everywhere: texts, sounds, log, spectra, images, biomedical data,
financial data, are described by hundreds or thousands of attributes. If we want to extract …

Dimension reduction for functional data based on weak conditional moments Page 1 The
Annals of Statistics 2022, Vol. 50, No. 1, 107–128 https://doi.org/10.1214/21-AOS2091 © …

The estimation of intrinsic dimensionality of high-dimensional data still remains a
challenging issue. Various approaches to interpret and estimate the intrinsic dimensionality …

Sufficient dimension reduction is a rapidly developing research field that has wide
applications in regression diagnostics, data visualization, machine learning, genomics …

For data with more variables than the sample size, phenomena like concentration of
pairwise distances, violation of cluster assumptions and presence of hubness often have …

Nonlinear sufficient dimension reduction for functional data Page 1 The Annals of Statistics
2017, Vol. 45, No. 3, 1059–1095 DOI: 10.1214/16-AOS1475 © Institute of Mathematical …