# Copyright 2021-2023 Lawrence Livermore National Security, LLC and other
# MuyGPyS Project Developers. See the top-level COPYRIGHT file for details.
#
# SPDX-License-Identifier: MIT
"""
Resources and high-level API for a simple regression workflow.
:func:`~MuyGPyS.examples.regress.make_regressor` is a high-level API for
creating and training :class:`MuyGPyS.gp.muygps.MuyGPS` objects for regression.
:func:`~MuyGPyS.examples.regress.make_multivariate_regressor` is a high-level
API for creating and training :class:`MuyGPyS.gp.muygps.MultivariateMuyGPS`
objects for regression.
:func:`~MuyGPyS.examples.regress.do_regress` is a high-level api for executing
a simple, generic regression workflow given data. It calls the maker APIs
above and :func:`~MuyGPyS.examples.regress.regress_any`.
"""
import numpy as np
from time import perf_counter
from typing import Dict, List, Tuple, Union
from MuyGPyS.examples.from_indices import regress_from_indices
from MuyGPyS.gp import MuyGPS, MultivariateMuyGPS as MMuyGPS
from MuyGPyS.gp.tensors import make_train_tensors
from MuyGPyS.neighbors import NN_Wrapper
from MuyGPyS.optimize import Bayes_optimize, OptimizeFn
from MuyGPyS.optimize.batch import sample_batch
from MuyGPyS.optimize.loss import LossFn, lool_fn
[docs]def make_regressor(
train_features: np.ndarray,
train_targets: np.ndarray,
nn_count: int = 30,
batch_count: int = 200,
loss_fn: LossFn = lool_fn,
opt_fn: OptimizeFn = Bayes_optimize,
k_kwargs: Dict = dict(),
nn_kwargs: Dict = dict(),
opt_kwargs: Dict = dict(),
verbose: bool = False,
) -> Tuple[MuyGPS, NN_Wrapper]:
"""
Convenience function for creating MuyGPyS functor and neighbor lookup data
structure.
Expected parameters include keyword argument dicts specifying kernel
parameters and nearest neighbor parameters. See the docstrings of the
appropriate functions for specifics.
Example:
>>> from MuyGPyS.examples.regress import make_regressor
>>> 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.examples.regress import make_regressor
>>> train_features, train_responses = make_train() # 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 = make_regressor(
... 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,
... )
Args:
train_features:
A matrix of shape `(train_count, feature_count)` whose rows consist
of observation vectors of the train data.
train_targets:
A matrix of shape `(train_count, response_count)` whose rows consist
of response vectors of the train data.
nn_count:
The number of nearest neighbors to employ.
batch_count:
The number of elements to sample batch for hyperparameter
optimization.
loss_fn:
The loss method to use in hyperparameter optimization. Ignored if
all of the parameters specified by argument `k_kwargs` are fixed.
opt_fn:
The optimization functor to use in hyperparameter optimization.
Ignored if all of the parameters specified by argument `k_kwargs`
are fixed.
k_kwargs:
Parameters for the kernel, possibly including kernel type,
deformation function, noise and scale hyperparameter specifications,
and specifications for kernel hyperparameters. See
:ref:`MuyGPyS-gp-kernels` for examples and requirements. If all of
the hyperparameters are fixed or are not given optimization bounds,
no optimization will occur.
nn_kwargs:
Parameters for the nearest neighbors wrapper. See
:class:`MuyGPyS.neighbors.NN_Wrapper` for the supported methods and
their parameters.
opt_kwargs:
Parameters for the wrapped optimizer. See the docs of the
corresponding library for supported parameters.
verbose:
If `True`, print summary statistics.
Returns
-------
muygps:
A (possibly trained) MuyGPs object.
nbrs_lookup:
A data structure supporting nearest neighbor queries into
`train_features`.
"""
train_count, _ = train_features.shape
_, response_count = train_targets.shape
time_start = perf_counter()
nbrs_lookup = NN_Wrapper(
train_features,
nn_count,
**nn_kwargs,
)
time_nn = perf_counter()
# create MuyGPs object
muygps = MuyGPS(**k_kwargs)
skip_opt = muygps.fixed()
if skip_opt is False:
# collect batch
batch_indices, batch_nn_indices = sample_batch(
nbrs_lookup,
batch_count,
train_count,
)
time_batch = perf_counter()
(
crosswise_diffs,
pairwise_diffs,
batch_targets,
batch_nn_targets,
) = make_train_tensors(
batch_indices,
batch_nn_indices,
train_features,
train_targets,
)
time_tensor = perf_counter()
if skip_opt is False:
# maybe do something with these estimates?
muygps = opt_fn(
muygps,
batch_targets,
batch_nn_targets,
crosswise_diffs,
pairwise_diffs,
loss_fn=loss_fn,
verbose=verbose,
**opt_kwargs,
)
time_opt = perf_counter()
muygps = muygps.optimize_scale(pairwise_diffs, batch_nn_targets)
if verbose is True:
print(f"Optimized scale values " f"{muygps.scale()}")
time_sopt = perf_counter()
if verbose is True:
print(f"NN lookup creation time: {time_nn - time_start}s")
print(f"batch sampling time: {time_batch - time_nn}s")
print(f"tensor creation time: {time_tensor - time_batch}s")
print(f"hyper opt time: {time_opt - time_tensor}s")
print(f"scale opt time: {time_sopt - time_opt}s")
return muygps, nbrs_lookup
[docs]def make_multivariate_regressor(
train_features: np.ndarray,
train_targets: np.ndarray,
nn_count: int = 30,
batch_count: int = 200,
loss_fn: LossFn = lool_fn,
opt_fn: OptimizeFn = Bayes_optimize,
k_args: Union[List[Dict], Tuple[Dict, ...]] = list(),
nn_kwargs: Dict = dict(),
opt_kwargs: Dict = dict(),
verbose: bool = False,
) -> Tuple[MMuyGPS, NN_Wrapper]:
"""
Convenience function for creating a Multivariate MuyGPyS functor and
neighbor lookup data structure.
Expected parameters include a list of keyword argument dicts specifying
kernel parameters and a dict listing nearest neighbor parameters. See the
docstrings of the appropriate functions for specifics.
Example:
>>> from MuyGPyS.examples.regress import make_multivariate_regressor
>>> 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
>>> train_features, train_responses = make_train() # stand-in function
>>> nn_kwargs = {"nn_method": "exact", "algorithm": "ball_tree"}
>>> k_args = [
... {
... "kernel": RBF(
... deformation=Isotropy(
... metric=F2,
... length_scale=Parameter(1.0, (1e-2, 1e2))
... )
... ),
... "noise": HomoscedasticNoise(1e-5),
... "scale": AnalyticScale(),
... },
... {
... "kernel": RBF(
... deformation=Isotropy(
... metric=F2,
... length_scale=Parameter(1.0, (1e-2, 1e2))
... )
... ),
... "noise": HomoscedasticNoise(1e-5),
... "scale": AnalyticScale(),
... },
... ]
>>> mmuygps, nbrs_lookup = make_multivariate_regressor(
... train_features,
... train_responses,
... nn_count=30,
... batch_count=200,
... loss_fn=lool_fn,
... opt_fn=Bayes_optimize,
... k_args=k_args,
... nn_kwargs=nn_kwargs,
... verbose=False,
... )
Args:
train_features:
A matrix of shape `(train_count, feature_count)` whose rows consist
of observation vectors of the train data.
train_targets:
A matrix of shape `(train_count, response_count)` whose rows consist
of response vectors of the train data.
nn_count:
The number of nearest neighbors to employ.
batch_count:
The number of elements to sample batch for hyperparameter
optimization.
loss_fn:
The loss method to use in hyperparameter optimization. Ignored if
all of the parameters specified by argument `k_kwargs` are fixed.
opt_fn:
The optimization functor to use in hyperparameter optimization.
Ignored if all of the parameters specified by argument `k_kwargs`
are fixed.
k_args:
A list of `response_count` dicts containing kernel initialization
keyword arguments. Each dict specifies parameters for the kernel,
possibly including noise and scale hyperparameter specifications
and specifications for specific kernel hyperparameters. If all of
the hyperparameters are fixed or are not given optimization bounds,
no optimization will occur.
nn_kwargs:
Parameters for the nearest neighbors wrapper. See
:class:`MuyGPyS.neighbors.NN_Wrapper` for the supported methods and
their parameters.
opt_kwargs:
Parameters for the wrapped optimizer. See the docs of the
corresponding library for supported parameters.
verbose:
If `True`, print summary statistics.
Returns
-------
mmuygps:
A Multivariate MuyGPs object with a separate (possibly trained) kernel
function associated with each response dimension.
nbrs_lookup:
A data structure supporting nearest neighbor queries into
`train_features`.
"""
train_count, response_count = train_targets.shape
if response_count != len(k_args):
raise ValueError(
f"supplied arguments for {len(k_args)} kernels, which does not "
f"match expected {response_count} responses!"
)
time_start = perf_counter()
nbrs_lookup = NN_Wrapper(
train_features,
nn_count,
**nn_kwargs,
)
time_nn = perf_counter()
# create MuyGPs object
mmuygps = MMuyGPS(*k_args)
skip_opt = mmuygps.fixed()
if skip_opt is False:
# collect batch
batch_indices, batch_nn_indices = sample_batch(
nbrs_lookup,
batch_count,
train_count,
)
time_batch = perf_counter()
(
crosswise_diffs,
pairwise_diffs,
batch_targets,
batch_nn_targets,
) = make_train_tensors(
batch_indices,
batch_nn_indices,
train_features,
train_targets,
)
time_tensor = perf_counter()
if skip_opt is False:
# maybe do something with these estimates?
for i, muygps in enumerate(mmuygps.models):
if muygps.fixed() is False:
mmuygps.models[i] = opt_fn(
muygps,
batch_targets[:, i].reshape(batch_targets.shape[0], 1),
batch_nn_targets[:, :, i].reshape(
batch_nn_targets.shape[0], nn_count, 1
),
crosswise_diffs,
pairwise_diffs,
loss_fn=loss_fn,
verbose=verbose,
**opt_kwargs,
)
time_opt = perf_counter()
mmuygps = mmuygps.optimize_scale(pairwise_diffs, batch_nn_targets)
if verbose is True:
print(f"Optimized scale values " f"{mmuygps.scale()}")
time_sopt = perf_counter()
if verbose is True:
print(f"NN lookup creation time: {time_nn - time_start}s")
print(f"batch sampling time: {time_batch - time_nn}s")
print(f"tensor creation time: {time_tensor - time_batch}s")
print(f"hyper opt time: {time_opt - time_tensor}s")
print(f"scale opt time: {time_sopt - time_opt}s")
return mmuygps, nbrs_lookup
def _empirical_covariance(train_targets: np.ndarray) -> np.ndarray:
"""
Convenience function computing the empirical covariance kernel between
multivariate response variables.
Args:
train_targets:
A matrix of shape `(train_count, response_count)` whose rows consist
of response vectors of the train data.
Returns:
An empirical covariance matrix of shape
`(response_count, response_count)`
"""
return np.cov(train_targets.T)
def _empirical_correlation(train_targets: np.ndarray) -> np.ndarray:
"""
Convenience function computing the empirical correlation kernel between
multivariate response variables.
Args:
train_targets:
A matrix of shape `(train_count, response_count)` whose rows consist
of response vectors of the train data.
Returns:
An empirical correlation matrix of shape
`(response_count, response_count)`
"""
return np.corrcoef(train_targets.T)
def _decide_and_make_regressor(
train_features: np.ndarray,
train_targets: np.ndarray,
nn_count: int = 30,
batch_count: int = 200,
loss_fn: LossFn = lool_fn,
opt_fn: OptimizeFn = Bayes_optimize,
k_kwargs: Union[Dict, Union[List[Dict], Tuple[Dict, ...]]] = dict(),
nn_kwargs: Dict = dict(),
opt_kwargs: Dict = dict(),
verbose: bool = False,
) -> Tuple[Union[MuyGPS, MMuyGPS], NN_Wrapper]:
if isinstance(k_kwargs, list) or isinstance(k_kwargs, tuple):
return make_multivariate_regressor(
train_features,
train_targets,
nn_count=nn_count,
batch_count=batch_count,
loss_fn=loss_fn,
opt_fn=opt_fn,
k_args=k_kwargs,
nn_kwargs=nn_kwargs,
opt_kwargs=opt_kwargs,
verbose=verbose,
)
else:
if isinstance(k_kwargs, dict):
return make_regressor(
train_features,
train_targets,
nn_count=nn_count,
batch_count=batch_count,
loss_fn=loss_fn,
opt_fn=opt_fn,
k_kwargs=k_kwargs,
nn_kwargs=nn_kwargs,
opt_kwargs=opt_kwargs,
verbose=verbose,
)
else:
raise ValueError("Expected k_kwargs to be a dict!")
def _unpack(first, *rest):
return first, rest
[docs]def do_regress(
test_features: np.ndarray,
train_features: np.ndarray,
train_targets: np.ndarray,
nn_count: int = 30,
batch_count: int = 200,
loss_fn: LossFn = lool_fn,
opt_fn: OptimizeFn = Bayes_optimize,
k_kwargs: Union[Dict, Union[List[Dict], Tuple[Dict, ...]]] = dict(),
nn_kwargs: Dict = dict(),
opt_kwargs: Dict = dict(),
verbose: bool = False,
) -> Tuple[Union[MuyGPS, MMuyGPS], NN_Wrapper, np.ndarray, np.ndarray]:
"""
Convenience function initializing a model and performing regression.
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, pass a list of hyperparameter dicts to `k_kwargs`.
Example:
>>> from MuyGPyS.examples.regress import do_regress
>>> 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.examples.regress import do_regress
>>> 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, variance = do_regress(
... 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,
... )
>>> mse = mse_fn(test_responses, predictions)
>>> print(f"obtained mse: {mse}")
obtained mse: 0.20842...
Args:
test_features:
A matrix of shape `(test_count, feature_count)` whose rows consist
of observation vectors of the test data.
train_features:
A matrix of shape `(train_count, feature_count)` whose rows consist
of observation vectors of the train data.
train_targets:
A matrix of shape `(train_count, response_count)` whose rows consist
of response vectors of the train data.
nn_count:
The number of nearest neighbors to employ.
batch_count:
The number of elements to sample batch for hyperparameter
optimization.
loss_fn:
The loss functor to use in hyperparameter optimization. Ignored if
all of the parameters specified by argument `k_kwargs` are fixed.
opt_fn:
The optimization functor to use in hyperparameter optimization.
Ignored if all of the parameters specified by argument `k_kwargs`
are fixed.
k_kwargs:
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
:func:`~MuyGPyS.examples.regress.make_multivariate_regressor`).
If given a dict, assume that the elements are keyword arguments to
a MuyGPs model (see
:func:`~MuyGPyS.examples.regress.make_regressor`).
nn_kwargs:
Parameters for the nearest neighbors wrapper. See
:class:`MuyGPyS.neighbors.NN_Wrapper` for the supported methods and
their parameters.
opt_kwargs:
Parameters for the wrapped optimizer. See the docs of the
corresponding library for supported parameters.
verbose:
If `True`, print summary statistics.
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.
variance:
Estimated `(test_count, response_count)` posterior variance of each
test prediction.
"""
regressor, nbrs_lookup = _decide_and_make_regressor(
train_features,
train_targets,
nn_count=nn_count,
batch_count=batch_count,
loss_fn=loss_fn,
opt_fn=opt_fn,
k_kwargs=k_kwargs,
nn_kwargs=nn_kwargs,
opt_kwargs=opt_kwargs,
verbose=verbose,
)
posterior_mean, posterior_variance, pred_timing = regress_any(
regressor,
test_features,
train_features,
nbrs_lookup,
train_targets,
)
return regressor, nbrs_lookup, posterior_mean, posterior_variance
[docs]def regress_any(
regressor: Union[MuyGPS, MMuyGPS],
test_features: np.ndarray,
train_features: np.ndarray,
train_nbrs_lookup: NN_Wrapper,
train_targets: np.ndarray,
) -> Tuple[np.ndarray, np.ndarray, Dict[str, float]]:
"""
Simultaneously predicts the response for each test item.
Args:
regressor:
Regressor object.
test_features:
Test observations of shape `(test_count, feature_count)`.
train_features:
Train observations of shape `(train_count, feature_count)`.
train_nbrs_lookup:
Trained nearest neighbor query data structure.
train_targets:
Observed response for all training data of shape
`(train_count, class_count)`.
Returns
-------
means:
The predicted response of shape `(test_count, response_count,)` for
each of the test examples.
variances:
The independent posterior variances for each of the test examples. Of
shape `(test_count,)` if the argument `regressor` is an instance of
:class:`MuyGPyS.gp.muygps.MuyGPS`, and of shape
`(test_count, response_count)` if `regressor` is an instance of
:class:`MuyGPyS.gp.muygps.MultivariateMuyGPS`.
timing : dict
Timing for the subroutines of this function.
"""
test_count, _ = test_features.shape
# train_count, _ = train_features.shape
time_start = perf_counter()
test_nn_indices, _ = train_nbrs_lookup.get_nns(test_features)
time_nn = perf_counter()
time_agree = perf_counter()
posterior_mean, posterior_variance = regress_from_indices(
regressor,
np.arange(test_count),
test_nn_indices,
test_features,
train_features,
train_targets,
)
time_pred = perf_counter()
timing = {
"nn": time_nn - time_start,
"agree": time_agree - time_nn,
"pred": time_pred - time_agree,
}
return posterior_mean, posterior_variance, timing