README.md

In rudazhang/plmr: Probabilistic Learning on Manifolds in R

Probabilistic Learning on Manifold

R pacakge plmr ("plumber") implements methods for Probabilistic Learning on Manifolds in R.

Installation

Install the developing verion via devtools.

if (!("devtools" %in% installed.packages()[,"Package"])) {
    install.packages(devtools)
}
devtools::install_github("rudazhang/plmr")

Manifest

Source code for package exported objects, /R:

• MParzen.R, manifold Parzen window [@Vincent2002] density estimation and sampling.
• SCMS.R, subspace-constrained mean shift [@Ozertem2011] and variants for ridge estimation.
• NormalBundleBootstrap.R, normal-bundle bootstrap (NBB) for inference in normal spaces of the density ridge, and data augmentation to reduce overfitting.
• DiffusionSampling.R, diffusion sampling on density ridge.
• DiffusionPropagate.R, heat diffusion on a manifold point cloud for probability propagation.
• ParameterizedManifolds.R, some parameterized manifolds and sampling.

Scripts for experiments and figures, /inst/script:

• nbb/, scripts for NBB.
  • 1-fig-scms-circle.R, script for SCMS with circle data;
  • 1-fig-scms-parabola.R, script for SCMS with parabola data;
  • 1-fig-exp-circle-ridge.R, script for circle;
  • 1-exp-wheel.R, script for wheel functional data, includes a rough implementation of NBB with smooth frame;
  • 1-fig-exp-wheel.R, plot wheel results;
• misc/, miscellaneous scripts:
  • exp-SCMS.R, ridge estimation by SCMS.
  • exp-diffusion-propagate.R, heat diffusion for probability propagation.
  • exp-earthquake.R, earthquake data.
  • exp-misc.R, miscellaneous toy examples.
  • exp-wasserstein.R, optimal transport and Wasserstein distances.

Documents, /vignettes:

• earthquake.md, earthquake data description.

References

• Data-driven probability concentration and sampling on manifold. C Soize, R Ghanem - Journal of Computational Physics, 2016. https://doi.org/10.1016/j.jcp.2016.05.044
• Normal-bundle Bootstrap. R Zhang, R Ghanem - arXiv, 2020. https://arxiv.org/abs/2007.13869

BibTeX citation:

@Article{ZhangRD2021nbb,
  author        = {Zhang, Ruda and Ghanem, Roger},
  title         = {Normal-Bundle Bootstrap},
  journal       = {SIAM Journal on Mathematics of Data Science},
  year          = {2021},
  volume        = {3},
  number        = {2},
  pages         = {573--592},
  doi           = {10.1137/20m1356002},
}

rudazhang/plmr documentation built on Aug. 30, 2021, 5:43 p.m.