fast_posterior_mean

Resources and high-level API for a fast posterior mean inference workflow.

make_fast_regressor() is a high-level API for creating the necessary components for fast posterior mean inference. make_fast_multivariate_regressor() is a high-level API for creating the necessary components for fast posterior mean inference with multiple outputs.

do_fast_posterior_mean() is a high-level api for executing a simple, generic fast posterior medan workflow given data. It calls the maker APIs above and fast_posterior_mean_any().

MuyGPyS.examples.fast_posterior_mean.do_fast_posterior_mean(test_features, train_features, train_targets, nn_count=30, batch_count=200, loss_fn=<MuyGPyS.optimize.loss.LossFn object>, opt_fn=<MuyGPyS.optimize.chassis.OptimizeFn object>, k_kwargs={}, nn_kwargs={}, opt_kwargs={}, verbose=False)[source]

Convenience function initializing a model and performing fast posterior mean inference.

Expected parameters include keyword argument dicts specifying kernel parameters and nearest neighbor parameters. See the docstrings of the appropriate functions for specifics.

Also supports workflows relying upon multivariate models. In order to create a multivariate model, specify the kern argument and pass a list of hyperparameter dicts to k_kwargs.

Example

>>> from MuyGPyS.testing.test_utils import _make_gaussian_data
>>> from MuyGPyS.examples.fast_posterior_mean import do_fast_posterior_mean
>>> from MuyGPyS.gp.deformation import F2, Isotropy
>>> from MuyGPyS.gp.hyperparameter import Parameter
>>> from MuyGPyS.gp.hyperparameter import AnalyticScale
>>> from MuyGPyS.gp.kernels import RBF
>>> from MuyGPyS.gp.noise import HomoscedasticNoise
>>> from MuyGPyS.optimize import Bayes_optimize
>>> from MuyGPyS.optimize.objective import mse_fn
>>> train_features, train_responses = make_train()  # stand-in function
>>> test_features, test_responses = make_test()  # stand-in function
>>> nn_kwargs = {"nn_method": "exact", "algorithm": "ball_tree"}
>>> k_kwargs = {
...     "kernel": RBF(
...         deformation=Isotropy(
...             metric=F2,
...             length_scale=Parameter(1.0, (1e-2, 1e2))
...         )
...     ),
...     "noise": HomoscedasticNoise(1e-5),
...     "scale": AnalyticScale(),
... }
>>> (
...     muygps, nbrs_lookup, predictions, precomputed_coefficients_matrix
... ) = do_fast_posterior_mean(
...         test_features,
...         train_features,
...         train_responses,
...         nn_count=30,
...         batch_count=200,
...         loss_fn=lool_fn,
...         opt_fn=Bayes_optimize,
...         k_kwargs=k_kwargs,
...         nn_kwargs=nn_kwargs,
...         verbose=False,
... )

Parameters:

test_features (ndarray) – A matrix of shape (test_count, feature_count) whose rows consist of observation vectors of the test data.
train_features (ndarray) – A matrix of shape (train_count, feature_count) whose rows consist of observation vectors of the train data.
train_targets (ndarray) – A matrix of shape (train_count, response_count) whose rows consist of response vectors of the train data.
nn_count (int) – The number of nearest neighbors to employ.
batch_count (int) – The number of elements to sample batch for hyperparameter optimization.
loss_fn (LossFn) – The loss functor to use in hyperparameter optimization. Ignored if all of the parameters specified by argument k_kwargs are fixed.
opt_fn (OptimizeFn) – The optimization functor to use in hyperparameter optimization. Ignored if all of the parameters specified by argument k_kwargs are fixed.
k_kwargs (Union[Dict, List[Dict], Tuple[Dict, ...]]) – If given a list or tuple of length response_count, assume that the elements are dicts containing kernel initialization keyword arguments for the creation of a multivariate model (see make_multivariate_regressor()). If given a dict, assume that the elements are keyword arguments to a MuyGPs model (see make_regressor()).
nn_kwargs (Dict) – Parameters for the nearest neighbors wrapper. See MuyGPyS.neighbors.NN_Wrapper for the supported methods and their parameters.
opt_kwargs (Dict) – Parameters for the wrapped optimizer. See the docs of the corresponding library for supported parameters.
verbose (bool) – If True, print summary statistics.

Return type:

Tuple[ndarray, NN_Wrapper, ndarray, ndarray, Dict]

Returns:

muygps – A (possibly trained) MuyGPs object.
nbrs_lookup – A data structure supporting nearest neighbor queries into train_features.
predictions – The predicted response associated with each test observation.
precomputed_coefficients_matrix – A matrix of shape (train_count, nn_count) whose rows list the precomputed coefficients for each nearest neighbors set in the training data.
timing – A dictionary containing timings for the training, precomputation, nearest neighbor computation, and prediction.

MuyGPyS.examples.fast_posterior_mean.fast_posterior_mean_any(muygps, test_features, train_features, nbrs_lookup, train_targets)[source]

Convenience function performing fast posterior mean inference using a pre-trained model.

Also supports workflows relying upon multivariate models.

Parameters:

muygps (Union[MuyGPS, MultivariateMuyGPS]) – A (possibly trained) MuyGPS object.
test_features (ndarray) – A matrix of shape (test_count, feature_count) whose rows consist of observation vectors of the test data.
train_features (ndarray) – A matrix of shape (train_count, feature_count) whose rows consist of observation vectors of the train data.
nbrs_lookup (NN_Wrapper) – A data structure supporting nearest neighbor queries into train_features.
train_targets (ndarray) – A matrix of shape (train_count, response_count) whose rows consist of response vectors of the train data.

Return type:

Tuple[ndarray, ndarray, Dict]

Returns:

posterior_mean – The predicted response associated with each test observation.
precomputed_coefficients_matrix – A matrix of shape (train_count, nn_count) whose rows list the precomputed coefficients for each nearest neighbors set in the training data.
timing – A dictionary containing timings for the training, precomputation, nearest neighbor computation, and prediction.

MuyGPyS.examples.fast_posterior_mean.make_fast_multivariate_regressor(mmuygps, nbrs_lookup, train_features, train_targets)[source]

Convenience function for creating precomputed coefficient matrix and neighbor lookup data structure.

Parameters:

muygps – A trained MultivariateMuyGPS object.
nbrs_lookup (NN_Wrapper) – A data structure supporting nearest neighbor queries into train_features.
train_features (ndarray) – A matrix of shape (train_count, feature_count) whose rows consist of observation vectors of the train data.
train_targets (ndarray) – A matrix of shape (train_count, response_count) whose rows consist of response vectors of the train data.

Return type:

Tuple[ndarray, ndarray]

Returns:

precomputed_coefficients_matrix – A matrix of shape (train_count, nn_count) whose rows list the precomputed coefficients for each nearest neighbors set in the training data.
nn_indices – An array supporting nearest neighbor queries.

MuyGPyS.examples.fast_posterior_mean.make_fast_regressor(muygps, nbrs_lookup, train_features, train_targets)[source]

Convenience function for creating precomputed coefficient matrix and neighbor lookup data structure.

Parameters:

muygps (MuyGPS) – A (possibly trained) MuyGPS object.
nbrs_lookup (NN_Wrapper) – A data structure supporting nearest neighbor queries into train_features.
train_features (ndarray) – A matrix of shape (train_count, feature_count) whose rows consist of observation vectors of the train data.
train_targets (ndarray) – A matrix of shape (train_count, response_count) whose rows consist of response vectors of the train data.

Return type:

Tuple[ndarray, ndarray]

Returns:

precomputed_coefficients_matrix – A matrix of shape (train_count, nn_count) whose rows list the precomputed coefficients for each nearest neighbors set in the training data.
nn_indices – A numpy.ndarrray supporting nearest neighbor queries.