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DNN weights: exact and asymptotic L-statistics

Source: vignettes/dnn-weights.Rmd
dnn-weights.Rmd

Overview

RdistNN provides two DNN rank-weight constructions:

  • method = "exact": finite-sample exact DNN coefficients
  • method = "asymp": asymptotic DNN coefficients

Use weights_dnn() to switch between them with a common interface.

Two support facts matter in practice:

  • exact DNN weights are computed from the full rank permutation for each target, not by keeping only the first s observations;
  • for the exact finite-population rule, support in rank order is j <= n - s + k, and in particular j <= n - s + 1 when k = 1;
  • the asymptotic Beta-increment approximation is typically treated as a full-support rank-weight sequence.

Fixed top-k DNN kernels are fully implemented for 1 <= k <= s. The fixed-k extension of the 1-NN theory is essentially direct, but the accompanying manuscript currently writes out the theoretical derivations only for k = 1.

Basic Usage 

n <- 150
p <- 2
X <- matrix(rnorm(n * p), n, p)
X0 <- matrix(rnorm(8), 4, p)

wt_exact <- weights_dnn(
  X = X, X0 = X0,
  distance = "l2",
  method = "exact",
  k = 1L, s = 4L,
  return = c("W", "ranks", "ord", "dx")
)

wt_asymp <- weights_dnn(
  X = X, X0 = X0,
  distance = "l2",
  method = "asymp",
  k = 1L, s = 4L,
  normalize = TRUE,
  return = "W"
)

colSums(wt_exact$W)
colSums(wt_asymp$W)

Single-target Convenience

Use x0 for one target instead of a one-row X0.

x0 <- c(0, 0)
wt_single <- weights_dnn(
  X = X, x0 = x0,
  method = "exact",
  k = 1L, s = 4L,
  return = c("W", "ranks")
)

dim(wt_single$W)  # n x 1

Working with Returned Diagnostics

return can include:

  • "W": weight matrix (n x m)
  • "ranks": rank matrix (n x m)
  • "ord": order matrix (n x m)
  • "dx": distance matrix (n x m)

These are useful when you want to:

  • verify deterministic ordering in tie settings
  • debug custom distance behavior
  • reuse ranks in downstream routines

Exact vs Asymptotic 

mu_signal <- rnorm(n)
mu_exact <- as.numeric(crossprod(mu_signal, wt_exact$W))
mu_asymp <- as.numeric(crossprod(mu_signal, wt_asymp$W))

cbind(mu_exact, mu_asymp)

For moderate samples and small s, exact weights are often preferred when you want finite-sample fidelity. Asymptotic weights can be cheaper and are often a practical default for larger-scale usage.