mixle.models.sparse_gaussian_process module

Inducing-point sparse Gaussian-process regression (FITC) – scalable GP inference.

Exact GP regression costs O(n^3) in the number of training points, which caps the field/emulator size for continental grids or large survey sets. This fits a sparse GP with m << n inducing points via the Fully Independent Training Conditional (FITC) approximation (Snelson & Ghahramani, 2006), costing O(n m^2 + m^3) – linear in n. As m -> n (and the inducing points cover the data) it recovers the exact GP. Part of the earth-science/multiphysics/UQ plan (Phase 3, scalable inference).

class SparseGaussianProcessRegressor(lengthscale=1.0, amplitude=1.0, noise=0.1, kernel='rbf', n_inducing=50)

Bases: object

Sparse GP regression with m inducing points (FITC).

Parameters:

• lengthscale – initial kernel/noise hyperparameters (all positive).

• amplitude – initial kernel/noise hyperparameters (all positive).

• noise – initial kernel/noise hyperparameters (all positive).

• kernel – 'rbf', 'matern32' or 'matern52'.

• n_inducing – number of inducing points (placed by k-means-lite over the training inputs at fit).

fit(x, y, *, optimize=True, seed=0, max_iter=100)

Place inducing points and (optionally) fit hyperparameters by the FITC marginal likelihood.

predict(x_new, *, return_var=False)

Posterior mean (and optionally marginal variance) at x_new. O(m^2) per query batch.