This implements the tuning procedure for SDR and classification problems in the forth coming paper Quach and Li (2021).
Usage
kfold_km_tuning(
h_list,
k,
x_datta,
y_datta,
d,
ytype,
class_labels,
n_cpc,
method = "newton",
std = "none",
parallelize = F,
control_list = list(),
iter.max = 100,
nstart = 100
)Arguments
- h_list
- k
- x_datta
- y_datta
- d
specified the reduced dimension
- ytype
specify the response as 'continuous', 'multinomial', or 'ordinal'
- class_labels
- n_cpc
- method
"newton" or "cg" methods; for carrying out the optimization using the standard newton-raphson (i.e. Fisher Scoring) or using Congugate Gradients
- parallelize
Default is False; to run in parallel, you will need to have foreach and some parallel backend loaded; parallelization is strongly recommended and encouraged.
- control_list
a list of control parameters for the Newton-Raphson or Conjugate Gradient methods
- iter.max
- nstart
Value
A list containing both the estimate and candidate matrix.
opcg - A 'pxd' matrix that estimates a basis for the central subspace.
opcg_wls - A 'pxd' matrix that estimates a basis for the central subspace based on the initial value of the optimization problem; useful for examining bad starting values.
cand_mat - A list that contains both the candidate matrix for OPCG and for the initial value; this is used in other functions for order determination
gradients - The estimated local gradients; used in regularization of OPCG
weights - The kernel weights in the local-linear GLM.
Details
The kernel for the local linear regression is fixed at a gaussian kernel.
For large 'p', we strongly recommend using the Conjugate Gradients implement, by setting method="cg". For method="cg", the hybrid conjugate gradient of Dai and Yuan is implemented, but only the armijo rule is implemented through backtracking, like in Bertsekas' "Convex Optimization Algorithms". A weak Wolfe condition can also be enforced by adding setting c_wolfe > 0 in the control_list, but since c_wolfe is usually set to 0.1 (Wikipedia) and this drastically slows down the algorithm relative to newton for small to moderate p, we leave the default as not enforcing a Wolfe condition, since we assume that our link function gives us a close enough initial point that local convergence is satisfactory. Should the initial values be suspect, then maybe enforcing the Wolfe condition is a reasonable trade-off.