himalaya.kernel_ridge.solve_weighted_kernel_ridge_gradient_descent

himalaya.kernel_ridge.solve_weighted_kernel_ridge_gradient_descent(Ks, Y, deltas, alpha=1.0, fit_intercept=False, step_sizes=None, lipschitz_Ks=None, initial_dual_weights=None, max_iter=100, tol=0.001, double_K=False, random_state=None, debug=False, n_targets_batch=None)

Solve weighted kernel ridge regression using gradient descent.

Solve the kernel ridge regression:

w* = argmin_w ||K @ w - Y||^2 + alpha (w.T @ K @ w)

where the kernel K is a weighted sum of multiple kernels:

K = sum_i exp(deltas[i]) Ks[i]

Parameters

Ksarray of shape (n_kernels, n_samples, n_samples)

Input kernels.

Yarray of shape (n_samples, n_targets)

Target data.

deltasarray of shape (n_kernels, ) or (n_kernels, n_targets)

Kernel weights.

alphafloat, or array of shape (n_targets, )

Regularization parameter.

fit_interceptboolean

Whether to fit an intercept. If False, Ks should be centered (see KernelCenterer), and Y must be zero-mean over samples.

step_sizesfloat, or array of shape (n_targets), or None

Step sizes. If None, computes a step size based on the Lipschitz constants.

lipschitz_Ksfloat, or array of shape (n_kernels), or None:

Lipschitz constant. Used only if step_sizes is None. If None, Lipschitz constants are estimated with power iteration on Ks.

initial_dual_weightsarray of shape (n_samples, n_targets)

Initial kernel ridge coefficients.

max_iterint

Maximum number of gradient step.

tolfloat > 0 or None

Tolerance for the stopping criterion.

double_Kbool

If True, multiply the gradient by the kernel to obtain the true gradients, which are less well conditionned.

random_stateint, or None

Random generator seed. Use an int for deterministic search.

debugbool

If True, check some intermediate computations.

n_targets_batchint or None

Size of the batch for over targets during cross-validation. Used for memory reasons. If None, uses all n_targets at once.

Returns

dual_weightsarray of shape (n_samples, n_targets)

Kernel ridge coefficients.

interceptarray of shape (n_targets,)

Intercept. Only returned when fit_intercept is True.