compute_rl_deriv_nn {GPCERF}

Calculate right minus left derivatives for change-point detection in nnGP

Description

Calculates the posterior mean of the difference between left- and right-derivatives at an exposure level for the detection of change points. nnGP approximation is used.

Usage

compute_rl_deriv_nn(
  w,
  w_obs,
  gps_m,
  y_obs,
  hyperparam,
  n_neighbor,
  block_size,
  kernel_fn = function(x) exp(-x),
  kernel_deriv_fn = function(x) -exp(-x)
)

Arguments

w

A scalar of exposure level of interest.

w_obs

A vector of observed exposure levels of all samples.

gps_m

An S3 gps object including: gps: A data.frame of GPS vectors. - Column 1: GPS - Column 2: Prediction of exposure for covariate of each data sample (e_gps_pred). - Column 3: Standard deviation of e_gps (e_gps_std) used_params: - dnorm_log: TRUE or FLASE

y_obs

A vector of observed outcome values.

hyperparam

A vector of hyper-parameters in the GP model.

n_neighbor

The number of nearest neighbors on one side.

block_size

The number of samples included in a computation block. Mainly used to balance the speed and memory requirement. Larger block_size is faster, but requires more memory.

kernel_fn

The covariance function. The input is the square of Euclidean distance.

kernel_deriv_fn

The partial derivative of the covariance function. The input is the square of Euclidean distance.

Value

A numeric value of the posterior mean of the difference between two one-sided derivatives.

Examples

set.seed(325)
data <- generate_synthetic_data(sample_size = 200)
gps_m <- estimate_gps(cov_mt = data[,-(1:2)],
                      w_all = data$treat,
                      sl_lib = c("SL.xgboost"),
                      dnorm_log = FALSE)

wi <- 12.2

deriv_val <- compute_rl_deriv_nn(w = wi,
                                 w_obs = data$treat,
                                 gps_m = gps_m,
                                 y_obs = data$Y,
                                 hyperparam = c(0.2,0.4,1.2),
                                 n_neighbor = 20,
                                 block_size = 10)