Mahalanobis distance spec (with one-time covariance setup)

Returns a distance spec that estimates the sample covariance from the training matrix X in setup(X), then evaluates $$d(X_i, x_0) = \sqrt{(X_i - x_0)^\top \hat\Sigma^{-1}(X_i - x_0)}$$ in eval() / eval_batch(). Requires at least two covariates.

Usage

distance_mahalanobis()

Value

A distance spec (list with name, setup, eval, eval_batch) for use with cate_dnn(), weights_dnn(), or register_distance(). The string alias "mahalanobis" is registered at package load.

Details

The covariance inverse is computed once in setup() and reused for all evaluations via the ctx argument, following the same convention as distance_l2_scaled(). When the sample covariance is (near-)singular a pseudoinverse via SVD is used automatically; no external packages are required.

Particularly useful for DGPs with correlated covariates (e.g.\ "dgp5_correlated") where L2 or diagonal-scaled L2 distances fail to adapt to the off-diagonal covariance structure.

See also

distance_l2(), distance_l2_scaled(), cate_dnn()

Examples

set.seed(1)
X  <- matrix(rnorm(100), 50, 2)
x0 <- c(0, 0)
dspec <- distance_mahalanobis()
ctx   <- dspec$setup(X)
head(dspec$eval(X, x0, ctx))
#> [1] 0.8446870 0.6615278 1.0527165 2.2075438 1.5473831 2.2365731