Kernel Order Tuning

Overview

RdistNN exposes kernel-order selection through a modular tuning API:

• build specs with new_tuning() or as_tuning(),
• register/reuse with register_tuning() and get_tuning(),
• evaluate defaults and candidate grids via tuning_eval();
• inspect resolved tuning metadata in fitted-object diagnostics.

Paper Default Undersmoothing Rule

The built-in rule is:

$$s(\lambda) = \left\lfloor \lambda\, n^{(k_x+1)/(k_x+2)} \right\rfloor$$

with finite-sample default lambda = 0.4 and default sensitivity grid lambda_grid = c(0.3, 0.4, 0.5, 0.75). The value lambda = 1 remains available as a more aggressive localization benchmark.

tun <- tuning_dnn_paper()
tuning_eval(tun, n = 1000, kx = 2, k = 1, mode = "default")
#> $s
#> [1] 71
#> 
#> $meta
#> $meta$lambda
#> [1] 0.4
#> 
#> $meta$formula
#> [1] "lambda * n^((kx + 1)/(kx + 2))"
#> 
#> $meta$rounding
#> [1] "floor"
#> 
#> $meta$name
#> [1] "paper_undersmooth"
#> 
#> $meta$n
#> [1] 1000
#> 
#> $meta$kx
#> [1] 2
#> 
#> 
#> $feasibility
#> $feasibility$k_le_s
#> [1] TRUE
#> 
#> $feasibility$s_lt_n
#> [1] TRUE

tuning_eval(tun, n = 1000, kx = 2, k = 1, mode = "grid")$candidates
#>   lambda   s feasible reason
#> 1   0.30  53     TRUE     ok
#> 2   0.40  71     TRUE     ok
#> 3   0.50  88     TRUE     ok
#> 4   0.75 133     TRUE     ok

Registry Usage

tuning_names()
#> [1] "paper_undersmooth"
get_tuning("paper_undersmooth")$name
#> [1] "paper_undersmooth"

Custom Rule

fixed12 <- as_tuning(function(...) 12L, name = "fixed_12")
tuning_eval(fixed12, n = 300, kx = 2, k = 1)
#> $s
#> [1] 12
#> 
#> $meta
#> $meta$name
#> [1] "fixed_12"
#> 
#> $meta$n
#> [1] 300
#> 
#> $meta$kx
#> [1] 2
#> 
#> 
#> $feasibility
#> $feasibility$k_le_s
#> [1] TRUE
#> 
#> $feasibility$s_lt_n
#> [1] TRUE

A custom rule can also return richer metadata:

meta_rule <- new_tuning(
  name = "meta_rule",
  eval = function(n, kx, k, se, jackknife, ctx = NULL) {
    list(
      s = floor(0.9 * n ^ ((kx + 1) / (kx + 2))),
      meta = list(
        lambda = 0.9,
        formula = "0.9 * n^((kx + 1)/(kx + 2))",
        rounding = "floor"
      )
    )
  }
)

tuning_eval(meta_rule, n = 500, kx = 2, k = 1)
#> $s
#> [1] 95
#> 
#> $meta
#> $meta$lambda
#> [1] 0.9
#> 
#> $meta$formula
#> [1] "0.9 * n^((kx + 1)/(kx + 2))"
#> 
#> $meta$rounding
#> [1] "floor"
#> 
#> $meta$name
#> [1] "meta_rule"
#> 
#> $meta$n
#> [1] 500
#> 
#> $meta$kx
#> [1] 2
#> 
#> 
#> $feasibility
#> $feasibility$k_le_s
#> [1] TRUE
#> 
#> $feasibility$s_lt_n
#> [1] TRUE

Wrapper Integration

High-level wrappers accept tuning = ... and resolve s internally:

demo <- np_demo_data(n = 200, p = 2, seed = 1)
fit <- np_dnn(
  data = demo$data,
  x_cols = c("X1", "X2"),
  y_col = "Y",
  x0 = demo$x0,
  k = 1,
  tuning = tuning_dnn_paper(),
  se = TRUE,
  return = c("W", "ess", "tuning")
)

fit$meta$s
#> [1] 21
fit$tuning$grid$candidates
#>   candidate_id computed_key is_default feasible reason status lambda  s
#> 1   lambda_0p3         s_15      FALSE     TRUE     ok     ok   0.30 15
#> 2   lambda_0p4         s_21       TRUE     TRUE     ok     ok   0.40 21
#> 3   lambda_0p5         s_26      FALSE     TRUE     ok     ok   0.50 26
#> 4  lambda_0p75         s_39      FALSE     TRUE     ok     ok   0.75 39
diagnostics(fit)[, c("target_id", "tuning_name", "tuning_default_s", "tuning_grid_n_candidates")]
#> <dnn_diagnostics>
#>   targets: 1
#>   dist   : available for 0/1 target(s)

Related Articles

• Notation and package conventions: vignette("notation-and-conventions", package = "RdistNN") relates s, k, lambda, support, and effective sample size to the paper notation.
• DNN weights: vignette("dnn-weights", package = "RdistNN") explains how the selected order enters exact and asymptotic weights.
• Diagnostics and reporting: vignette("diagnostics-reporting", package = "RdistNN") shows how resolved tuning metadata appears in fitted-object diagnostics.