Conditional Density Estimation with Homoskedasticity Assumption

This function accepting an mean_lnr, which it then trains on the data and formula given. Then stats::density is fit to the error (difference between observed outcome and the mean_lnr predictions).

Usage

lnr_homoskedastic_density(
  data,
  formula,
  mean_lnr,
  mean_lnr_args = NULL,
  density_args = NULL
)

Arguments

data: A dataframe to train a learner / learners on.
formula: A regression formula to use inside this learner.
mean_lnr: A learner (function) passed in to be trained on the data with the given formula and then used to predict conditional means for provided newdata.
mean_lnr_args: Extra arguments to be passed to the mean_lnr
density_args: Extra arguments to be passed to the kernel density smoother stats::density, especially things like bw for specifying the smoothing bandwidth. See ?stats::density.

Value

A predictor function that takes in newdata and produces density estimates

Details

This returns a function that takes in newdata and produces density estimates according to the estimated stats::density fit the error from the newdata observed outcome and the prediction from the mean_lnr.

That is to say, this follows the following procedure (assuming $Y$ as the outcome and $X$ as a matrix of predictors):

$$\texttt{obtain } \hat{\mathbb E}(Y | X) \quad \mathtt{using \quad mean\_learner}$$ $$\texttt{fit } \hat{f} \gets \mathtt{density}(Y - \hat{\mathbb E}(Y | X))$$ $$\mathtt{return \quad function(newdata) \{ } \hat{f}(\mathtt{newdata\$Y} - \hat{\mathbb E}[Y | \mathtt{newdata\$X}]) \} $$

Examples

if (FALSE) { # \dontrun{
# fit a conditional density model with mean model as a randomForest
fit_density_lnr <- lnr_homoskedastic_density(
  data = mtcars,
  formula = mpg ~ hp,
  mean_lnr = lnr_rf)

# and what we should get back should be predicted densities at the
# observed mpg given the covariates hp
fit_density_lnr(mtcars)
} # }