The prediction averaged over the observed joint distribution of the
complement variables, with the variables in S held fixed. This is a
marginal of the FITTED surface, not a conditional expectation: it answers
"what does the model do if I move x_S", not "what is E of y given x_S".
Usage
morie_esl_partial_dependence(model, X, S, grid = NULL, n_grid = 20L)
Arguments
- model
Function taking an (m, p) matrix and returning predictions.
- X
Data supplying the complement distribution, n by p.
- S
Column indices (1-based) to vary.
- grid
Values of x_S to evaluate; defaults to a quantile grid.
- n_grid
Grid size when grid is not given.
Value
List with grid, pd, centered, extrapolation_warning.
Details
The average runs over the marginal of the complement, so when x_S and the
complement are correlated the model is evaluated at combinations that never
occur, and the curve there is extrapolation. extrapolation_warning flags
grid points whose synthetic rows sit far from the observed cloud –
measured in the JOINT, since every quantile grid point is by construction
close to observed x_S values.
References
Friedman, J. H. (2001). Greedy function approximation.
Annals of Statistics 29(5), 1189-1232.
Examples
set.seed(1)
X <- matrix(runif(800, -2, 2), ncol = 2)
f <- function(Z) 3 * Z[, 1] + Z[, 2]^2
r <- morie_esl_partial_dependence(f, X, S = 1, n_grid = 9)
abs(stats::coef(stats::lm(r$pd ~ r$grid[, 1]))[[2]] - 3) < 1e-8
#> [1] TRUE
