GpFlash for Python
Fast, exact Gaussian process regression: the marginal log likelihood (MLL) with analytic hyperparameter gradients, hyperparameter fitting, and posterior mean and variance. Python bindings to the header-only C++ library GpFlash.
pip install gpflash
Wheels are available for Linux (x86_64, aarch64), macOS (arm64, x86_64) and Windows (x64), on Python 3.11 to 3.14. They need nothing else installed: BLAS/LAPACK, HDF5, NLopt and the OpenMP runtime are included.
Quick start
import numpy as np
import gpflash
rng = np.random.default_rng(0)
X = rng.random((50, 2)) # (n_points, n_dim)
y = np.sin(3 * X[:, 0]) + X[:, 1] ** 2
gp = gpflash.GaussianProcess("matern_5_2").fit(X, y)
mean, var = gp.predict(rng.random((100, 2)), return_var=True)
print(gp.summary()) # MLL, optimality, evaluations, bounds hit
print(gp.hyperparameters_) # sig2_k, sig2_f, gamma, kern_extra, beta
GaussianProcess
| Argument | Meaning |
|---|---|
kernel |
"sq_exp", "matern_5_2" (default), "matern_3_2", "rat_quad", "periodic", "linear", "quadratic" |
noise |
0.0 for noise-free data (default), a known variance, or "estimate" to fit it |
mean |
"constant" (default) or "zero"; the weights are solved in closed form |
n_starts |
Local optimizations; above 1, the extra starts are Latin-hypercube samples, and the best fit is kept |
seed |
Seed for those starts, so a fit is reproducible |
GaussianProcess.from_options(optz_options, noise=...) takes an OptzOptions instead, for full
control of the fit: bounds, tolerances, the algorithm, symmetry, mean model degrees.
| Method | Returns |
|---|---|
fit(X, y) |
self; X is (n_points, n_dim) |
predict(X, return_var=False) |
The posterior mean, and the variance when asked |
predict_gradient(X) |
The gradients of the mean and variance, each (n_points, n_dim) |
save(path) / GaussianProcess.load(path) |
An HDF5 file the C++ library also reads |
summary() |
A short report of the fit |
A noise-free fit adds a small nugget, sized from ModelOptions.cond_max, so the factorization is
always well conditioned; predictions at the training points then match the data closely rather
than exactly.
The C++ interface
Everything in the C++ library is also available under its C++ names: TrainingData, HpVal,
ModelOptions, OptzOptions, eval_mll, select_hp_with_max_mll, make_posterior,
GpPosterior, load_posterior and the rest, so the
C++ README documents this layer too. It keeps the
C++ shapes: points are columns, so TrainingData.X_ndim_ntrain_mat is (n_dim, n_train).
train_data = gpflash.TrainingData()
train_data.X_ndim_ntrain_mat = X.T # (n_dim, n_train)
train_data.f_train_vec = y
hp_val = gpflash.HpVal()
hp_val.hp_gamma_vec = [1.0, 1.0] # inverse length scales
mll_result = gpflash.eval_mll(train_data, hp_val, gpflash.ModelOptions(), return_mll_gradient=True)
print(mll_result.mll, mll_result.mll_hp_grad_struct.d_mll_d_hp_gamma_vec)
Array fields are copied in and out, so assign a whole array to change one:
hp_val.hp_gamma_vec = new_values works; hp_val.hp_gamma_vec[0] = 2.0 changes only a copy.
Invalid inputs raise gpflash.InvalidInputError, a ValueError. Numerical failures raise
gpflash.NumericalFailureError, an ArithmeticError.
Inspecting a fit and a saved file
fit = gp.fit_result_ # an MllOptzResult
fit.build_best_local_optz_result().stop_reason # why the winning solve stopped
fit.calc_hp_at_bound_struct().to_summary_string() # which hyperparameters a bound holds
gpflash.print_multistart_report(fit) # every optimization, where each started and landed
info = gpflash.peek_info("model.h5") # the file's header, without loading it
gpflash.print_cache_info(info) # kernel, MLL, size, note, writing version
save_multistart_report writes the report to a file. GpPosterior.post_model_info() is the
record of the fit a posterior came from, and calc_default_cache_path names a file after the
kernel and the training set's shape. Because None is a Python keyword, SymmetryKind's
no-symmetry value is SymmetryKind.None_.
The one C++ feature the Python package leaves out is MPI: a fit runs in one process, using its cores through OpenMP.
Threads
Fits and queries run in parallel with OpenMP and release the GIL, so other Python threads run
meanwhile. OMP_NUM_THREADS sets the thread count. Loading two different OpenMP runtimes into
one process, for example GpFlash's alongside another library's, can slow both down; if that
happens, set OMP_NUM_THREADS or import one library at a time.
Building from source
pip install . from a clone of the repository builds the module with CMake. It needs a C++14
compiler and the C++ library's dependencies; the
C++ README lists them per platform. On macOS,
point CMake at Homebrew's OpenMP:
CMAKE_ARGS="-DOpenMP_ROOT=$(brew --prefix libomp)" pip install ".[test]"
pytest python/tests
After changing python/src/bindings.cpp, regenerate the type stubs with
pybind11-stubgen gpflash._core -o python (it writes python/gpflash/_core.pyi), then change the
__version__ line it writes to __version__: str, so the stub carries no copy of the version.
Citing
If you use GpFlash, please cite the paper, arXiv:2610.16861:
@misc{marchildon2026gpflash,
title = {GpFlash: Maximizing Speed and Minimizing Memory for Gaussian Process Training and Prediction},
author = {Marchildon, Andr{\'e}},
year = {2026},
eprint = {2610.16861},
archivePrefix = {arXiv},
primaryClass = {cs.LG},
doi = {10.48550/arXiv.2610.16861}
}
License
Apache License 2.0. The wheels also contain compiled third-party libraries under their own
licenses; LICENSES_bundled.txt, installed with the package metadata, reproduces them.
1 maintainer
Metadata
1 maintainer
Release files for gpflash 0.2.0
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