TDNN weights (exact, k = 1), distance-based ranking

Computes Demirkaya two-scale DNN (TDNN) weights using the exact rank-weight table (tdnn_rank_table_exact()). TDNN is a signed linear combination of two single-scale exact DNN tables at orders s1 and s2; the combination coefficients are chosen to cancel the leading bias term in the DNN MSE expansion.

Usage

weights_tdnn_exact(
  X,
  X0 = NULL,
  x0 = NULL,
  distance = "l2",
  s1,
  s2,
  dim = NULL,
  ctx = NULL,
  return = c("W")
)

Arguments

X

Numeric matrix (n x p).

X0

Numeric matrix (m x p); mutually exclusive with x0.

x0

Numeric length-p single target (convenience for m = 1).

distance

Distance spec or registered name (e.g., "l2").

s1

Positive integer; smaller U-statistic order (s1 < s2 <= n).

s2

Positive integer; larger U-statistic order.

dim

Positive integer; localization dimension. Defaults to ncol(X) when NULL.

ctx

Optional context passed through to distance and rank-weight evaluators.

return

Character vector of extras to include; any of c("W", "ord", "ranks", "dx").

Value

A weights_result object (same structure as weights_dnn_exact()).

Details

Signed weights. The returned weight matrix W can contain negative entries; columns still sum to 1. This is by design and reflects the bias-correction structure of TDNN.

See also

weights_tdnn_asymp(), weights_tdnn(), rank_weight_tdnn_exact()

Examples

set.seed(1)
X  <- matrix(rnorm(30), 15, 2)
x0 <- c(0, 0)
out <- weights_tdnn_exact(X, x0 = x0, s1 = 3L, s2 = 6L)
colSums(out$W)  # 1
#> [1] 1
any(out$W < 0)  # TRUE
#> [1] TRUE