Kernel Quantile Regression

TorchKM includes kernel quantile regression for continuous targets through TorchKMKQR.

Basic usage

import numpy as np
import torch

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

from torchkm.estimators import TorchKMKQR

X, y = make_regression(
    n_samples=100,
    n_features=5,
    noise=0.5,
    random_state=0,
)
X = StandardScaler().fit_transform(X)

Xtr, Xte, ytr, yte = train_test_split(X, y, test_size=0.25, random_state=0)

Cs = np.logspace(2, -2, num=3)
device = "cuda" if torch.cuda.is_available() else "cpu"

reg = TorchKMKQR(
    kernel="rbf",
    Cs=Cs,
    nC=len(Cs),
    cv=5,
    tau=0.5,
    device=device,
    random_state=0,
    max_iter=80,
)

reg.fit(Xtr, ytr)
pred = reg.predict(Xte)

print("best C:", reg.best_C_)
print("first predictions:", pred[:3])

Important parameters

Parameter	Description
kernel	Kernel type for TorchKMKQR: "rbf", "linear", "poly", or "precomputed"
tau	Quantile level in (0, 1)
Cs	Candidate regularization values under the C convention
nC	Number of candidate values when Cs is not supplied
cv	Number of cross-validation folds
device	"cpu", "cuda", or None for automatic selection
max_iter	Maximum solver iterations
low_rank	Use the Nyström approximation through cvknyqr
num_landmarks, nys_k	Landmark count and Nyström rank when low_rank=True

Constructor-based low-rank configuration is recommended, but TorchKMKQR.fit also accepts low_rank, num_landmarks, and nys_k as keyword-only convenience arguments.

Fitted attributes

After fitting, useful attributes include:

• best_C_: selected regularization value;
• best_ind_: selected grid index;
• cv_loss_: cross-validation check-loss values;
• alpha_ and intercept_: selected model coefficients;
• foldid_: fold assignment used during fitting.

Low-level solver

Advanced users can access the lower-level solver directly:

from torchkm.cvkqr import cvkqr
from torchkm.cvknyqr import cvknyqr

cvkqr handles full-kernel quantile regression, and cvknyqr provides the Nyström solver. See the low-level solver API for exact signatures.