Friedman-Tukey projection pursuit regression as in ESL Sec 11.2 (eqs
11.1-11.4): terms are added forward stage-wise; each alternates a cubic
smoothing spline of the residual on the projection with the Gauss-Newton
direction update (weighted least squares with weights g'^2, solved as the
equivalent regression of g' v + r - g on g' x), halving the step if the
residual sum of squares rises. The ridge functions are readjusted by
backfitting after each new term; the directions are not.
Usage
morie_esl_projection_pursuit(
X,
y,
M = 2,
penalty = 1,
max_iter = 50,
tol = 1e-08,
backfit = 10,
newdata = NULL
)
Arguments
- X
Numeric matrix, N by p.
- y
Response vector.
- M
Number of ridge terms.
- penalty
Smoothing-spline penalty (> 0) on the projection scale.
- max_iter, tol
Gauss-Newton controls per term.
- backfit
Maximum backfitting passes after each term.
- newdata
Optional matrix of points to predict.
Value
Named list: omega, fitted, residuals, rss, rss_path, intercept,
terms, predicted.
References
Friedman, J. H. & Tukey, J. W. (1974). IEEE Trans. Computers
C-23, 881-890.
Examples
X <- cbind((0:20) / 5 - 2, ((7 * (0:20)) %% 11) / 5 - 1)
morie_esl_projection_pursuit(X, rowSums(X)^2, M = 1, penalty = 0.01)$omega
#> [[1]]
#> [1] -0.7076162 -0.7065970
#>
