Minimal nonparametric regression demo data (oracle m and Y only)

Generates a simple nonparametric regression dataset with features \(X\) and response \(Y = m(X) + \epsilon\), returning the oracle regression function \(m(x)\). This is designed for experimenting with the Y-only singleton score score_np_y().

Usage

np_demo_data(
  n = 200,
  p = 2,
  design = c("linear", "sinusoidal", "bump", "constant"),
  sigma = 0.5,
  seed = NULL,
  x0 = NULL,
  inject = NULL,
  idx_inject = 3L
)

Arguments

n: Integer; sample size.
p: Integer; number of features in \(X\).
design: Character; one of "linear", "sinusoidal", "bump", "constant".
sigma: Noise standard deviation in \(Y\).
seed: Optional integer seed for reproducibility.
x0: Optional target point in \(\mathbb{R}^p\) (defaults to the zero vector).
inject: Optional, one of NULL, "na", "inf"; if provided, inject a single non-finite value into Y at idx_inject (useful for tests).
idx_inject: Integer index at which to inject NA/Inf (default 3).

Value

A list with:

data: data.frame with columns X1..Xp, Y, and m_oracle (=\(m(X)\)).
x0: the target point used.
truth: list with closure m_fn(x) for evaluating \(m(x)\) at new \(X\).
m_x0: the true \(m(x_0)\).

Examples

demo <- np_demo_data(n = 200, p = 2, design = "sinusoidal", seed = 1)
head(demo$data)
#>           X1         X2           Y   m_oracle
#> 1 -0.6264538  0.4094018  0.28598513 -0.2512354
#> 2  0.1836433  1.6888733  1.75220705  0.8043797
#> 3 -0.8356286  1.5865884 -0.04304208  0.2584566
#> 4  1.5952808 -0.3309078  0.33179122  0.5272251
#> 5  0.3295078 -2.2852355  1.25925301  1.4673640
#> 6 -0.8204684  2.4976616  1.00601700  1.1938457
demo$m_x0
#> [1] 0