/BootstrapAsymptotics

Code for the paper "Analysis of Bootstrap and Subsampling in High-dimensional Regularized Regression"

Primary LanguageJupyter Notebook

BootstrapAsymptotics

Dev Build Status Code Style: Blue

Code for the paper

Getting started

Open a Julia console and run:

julia> using Pkg

julia> Pkg.add(url="https://github.com/SPOC-group/BootstrapAsymptotics")

Using the package

julia> using BootstrapAsymptotics

julia> (; overlaps) = state_evolution(Ridge(λ=0.1), PairBootstrap(), PairBootstrap());

julia> Matrix(overlaps.Q)
2×2 Matrix{Float64}:
 1.35642   0.799808
 0.799808  1.35642

Reproducing the plots

Open the Jupyter notebooks in the experiments folder, select the Julia environment defined in the same folder, and run.

Computing the large $\alpha$ rates

Open the Mathematica notebook experiments/large_alpha_rates.nb

Notations

  • n: number of samples
  • d: dimension
  • α: sampling ratio n/d
  • Δ: noise variance
  • λ: regularization parameter
  • m, Q, V: overlaps