predict returns invalid density estimates when trim=TRUE (the default)

[jeremyrcoyle]

The density estimates from predict can integrate to more than 1 when trimming is enabled. Perhaps some renormalization is needed after trimming?

# example from the docs
set.seed(1234)
n_train <- 50
w <- runif(n_train, -4, 4)
a <- rnorm(n_train, w, 0.5)
# HAL-based density estimator of A|W
haldensify_fit <- haldensify(
  A = a, W = w, n_bins = 10L, lambda_seq = exp(seq(-1, -10, length = 100)),
  # the following arguments are passed to hal9001::fit_hal()
  max_degree = 5, smoothness_orders = 0, num_knots = NULL,
  reduce_basis = 1 / sqrt(length(a))
)
# predictions to recover conditional density of A|W
new_a <- seq(-4, 4, by = 0.1)
new_w <- rep(0, length(new_a))

# the density integrates to much more than 1
pred_dens <- predict(haldensify_fit, new_A = new_a, new_W = new_w)
pracma::trapz(new_a, pred_dens)
# 1.4869

# the density integrates to ~ 1 with trim = FALSE
pred_dens2 <- predict(haldensify_fit, new_A = new_a, new_W = new_w, trim = FALSE)
pracma::trapz(new_a, pred_dens2)
# 0.9955347