Overview

This repository provides R Source codes to reproduce numerical experiments in the following paper:

@article{okuno2024NPIR,
    year      = {2024},
    publisher = {},
    volume    = {18},
    number    = {1},
    pages     = {355-394},
    author    = {Akifumi Okuno and Masaaki Imaizumi},
    title     = {Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regression},
    journal   = {Electronic Journal of Statistics},
    doi       = {10.1214/23-EJS2202}
}

1_NPIR.R

Computes nonparametric planer invertible regression. The results are saved into (automatically-generated) output folder.

This script estimates the invertible function by the following procedure:

• For I=[-1,1], generate x1,x2,...,xn uniformly randomly from I^2, and also generate y1,y2,...,yn \in I^2 fandomly from a normal distribution N(f(xi),vI). These (x_i,y_i) are used for experiments.
• Compute a first step estimator f^{(1)}(x) using k-nearest neighbour
• Empirically estimate the homeomorphism \rho (via estimation of the rotation of the four-vertices of I)
• After estimating g = \rho \circ f^{(1)}, define coherent_g which slightly fixes the four vertices
• Using the coherent_g, define g_dagger which smoothly interpolates the internal region (of each triangle connecting vertices)
• Compute the proposed estimator f^{(2)} = \rho^{-1} \circ g_\dagger

Experimental results for a function (whose level set includes twists) are saved into OUTPUT/TWIST. Those for a function whose level set does not include twists (i.e., its estimation is easier) are saved into OUTPUT/NON_TWIST.

Output 1 (P1): Rotation that matches the four vertices of I^2

Output 2 (P2): Influence of the precision parameter t to the estimation of the function f

Output 3 (P3): Visualization of each step of the estimation

Output 4 (P4): Grid used in the function estimation

2_TrueLevelSets.R

Output 5 (P5): Visualization of the level-set for the underlying true function f*

A_functions.R

This script contains several functions to be called from the above scripts.