agtboost (version 0.9.3)

gbt.ksval: Kolmogorov-Smirnov validation of model

Description

gbt.ksval transforms observations to U(0,1) if the model is correct and performs a Kolmogorov-Smirnov test for uniformity.

Usage

gbt.ksval(object, y, x)

Arguments

object

Object or pointer to object of class ENSEMBLE

y

Observations to be tested

x

design matrix for training. Must be of type matrix.

Value

Kolmogorov-Smirnov test of model

Details

Model validation of model passed as object using observations y. Assuming the loss is a negative log-likelihood and thus a probabilistic model, the transformation $$u = F_Y(y;x,\theta) \sim U(0,1),$$ is usually valid. One parameter, \(\mu=g^{-1}(f(x))\), is given by the model. Remaining parameters are estimated globally over feature space, assuming they are constant. This then allow the above transformation to be exploited, so that the Kolmogorov-Smirnov test for uniformity can be performed.

If the response is a count model (poisson or negbinom), the transformation $$u_i = F_Y(y_i-1;x,\theta) + Uf_Y(y_i,x,\theta), ~ U \sim U(0,1)$$ is used to obtain a continuous transformation to the unit interval, which, if the model is correct, will give standard uniform random variables.

Examples

# NOT RUN {
## Gaussian regression:
x_tr <- as.matrix(runif(500, 0, 4))
y_tr <- rnorm(500, x_tr, 1)
x_te <- as.matrix(runif(500, 0, 4))
y_te <- rnorm(500, x_te, 1)
mod <- gbt.train(y_tr, x_tr)
gbt.ksval(mod, y_te, x_te)

# }