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"""Gaussian processes classification."""
# Authors: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
#
# License: BSD 3 clause
from operator import itemgetter
import numpy as np
from scipy.linalg import cholesky, cho_solve, solve
import scipy.optimize
from scipy.special import erf, expit
from ..base import BaseEstimator, ClassifierMixin, clone
from .kernels \
import RBF, CompoundKernel, ConstantKernel as C
from ..utils.validation import check_is_fitted, check_array
from ..utils import check_random_state
from ..utils.optimize import _check_optimize_result
from ..preprocessing import LabelEncoder
from ..multiclass import OneVsRestClassifier, OneVsOneClassifier
from ..utils.validation import _deprecate_positional_args
# Values required for approximating the logistic sigmoid by
# error functions. coefs are obtained via:
# x = np.array([0, 0.6, 2, 3.5, 4.5, np.inf])
# b = logistic(x)
# A = (erf(np.dot(x, self.lambdas)) + 1) / 2
# coefs = lstsq(A, b)[0]
LAMBDAS = np.array([0.41, 0.4, 0.37, 0.44, 0.39])[:, np.newaxis]
COEFS = np.array([-1854.8214151, 3516.89893646, 221.29346712,
128.12323805, -2010.49422654])[:, np.newaxis]
class _BinaryGaussianProcessClassifierLaplace(BaseEstimator):
"""Binary Gaussian process classification based on Laplace approximation.
The implementation is based on Algorithm 3.1, 3.2, and 5.1 of
``Gaussian Processes for Machine Learning'' (GPML) by Rasmussen and
Williams.
Internally, the Laplace approximation is used for approximating the
non-Gaussian posterior by a Gaussian.
Currently, the implementation is restricted to using the logistic link
function.
.. versionadded:: 0.18
Parameters
----------
kernel : kernel instance, default=None
The kernel specifying the covariance function of the GP. If None is
passed, the kernel "1.0 * RBF(1.0)" is used as default. Note that
the kernel's hyperparameters are optimized during fitting.
optimizer : 'fmin_l_bfgs_b' or callable, default='fmin_l_bfgs_b'
Can either be one of the internally supported optimizers for optimizing
the kernel's parameters, specified by a string, or an externally
defined optimizer passed as a callable. If a callable is passed, it
must have the signature::
def optimizer(obj_func, initial_theta, bounds):
# * 'obj_func' is the objective function to be maximized, which
# takes the hyperparameters theta as parameter and an
# optional flag eval_gradient, which determines if the
# gradient is returned additionally to the function value
# * 'initial_theta': the initial value for theta, which can be
# used by local optimizers
# * 'bounds': the bounds on the values of theta
....
# Returned are the best found hyperparameters theta and
# the corresponding value of the target function.
return theta_opt, func_min
Per default, the 'L-BFGS-B' algorithm from scipy.optimize.minimize
is used. If None is passed, the kernel's parameters are kept fixed.
Available internal optimizers are::
'fmin_l_bfgs_b'
n_restarts_optimizer : int, default=0
The number of restarts of the optimizer for finding the kernel's
parameters which maximize the log-marginal likelihood. The first run
of the optimizer is performed from the kernel's initial parameters,
the remaining ones (if any) from thetas sampled log-uniform randomly
from the space of allowed theta-values. If greater than 0, all bounds
must be finite. Note that n_restarts_optimizer=0 implies that one
run is performed.
max_iter_predict : int, default=100
The maximum number of iterations in Newton's method for approximating
the posterior during predict. Smaller values will reduce computation
time at the cost of worse results.
warm_start : bool, default=False
If warm-starts are enabled, the solution of the last Newton iteration
on the Laplace approximation of the posterior mode is used as
initialization for the next call of _posterior_mode(). This can speed
up convergence when _posterior_mode is called several times on similar
problems as in hyperparameter optimization. See :term:`the Glossary
<warm_start>`.
copy_X_train : bool, default=True
If True, a persistent copy of the training data is stored in the
object. Otherwise, just a reference to the training data is stored,
which might cause predictions to change if the data is modified
externally.
random_state : int or RandomState, default=None
Determines random number generation used to initialize the centers.
Pass an int for reproducible results across multiple function calls.
See :term: `Glossary <random_state>`.
Attributes
----------
X_train_ : array-like of shape (n_samples, n_features) or list of object
Feature vectors or other representations of training data (also
required for prediction).
y_train_ : array-like of shape (n_samples,)
Target values in training data (also required for prediction)
classes_ : array-like of shape (n_classes,)
Unique class labels.
kernel_ : kernl instance
The kernel used for prediction. The structure of the kernel is the
same as the one passed as parameter but with optimized hyperparameters
L_ : array-like of shape (n_samples, n_samples)
Lower-triangular Cholesky decomposition of the kernel in X_train_
pi_ : array-like of shape (n_samples,)
The probabilities of the positive class for the training points
X_train_
W_sr_ : array-like of shape (n_samples,)
Square root of W, the Hessian of log-likelihood of the latent function
values for the observed labels. Since W is diagonal, only the diagonal
of sqrt(W) is stored.
log_marginal_likelihood_value_ : float
The log-marginal-likelihood of ``self.kernel_.theta``
"""
@_deprecate_positional_args
def __init__(self, kernel=None, *, optimizer="fmin_l_bfgs_b",
n_restarts_optimizer=0, max_iter_predict=100,
warm_start=False, copy_X_train=True, random_state=None):
self.kernel = kernel
self.optimizer = optimizer
self.n_restarts_optimizer = n_restarts_optimizer
self.max_iter_predict = max_iter_predict
self.warm_start = warm_start
self.copy_X_train = copy_X_train
self.random_state = random_state
def fit(self, X, y):
"""Fit Gaussian process classification model
Parameters
----------
X : array-like of shape (n_samples, n_features) or list of object
Feature vectors or other representations of training data.
y : array-like of shape (n_samples,)
Target values, must be binary
Returns
-------
self : returns an instance of self.
"""
if self.kernel is None: # Use an RBF kernel as default
self.kernel_ = C(1.0, constant_value_bounds="fixed") \
* RBF(1.0, length_scale_bounds="fixed")
else:
self.kernel_ = clone(self.kernel)
self.rng = check_random_state(self.random_state)
self.X_train_ = np.copy(X) if self.copy_X_train else X
# Encode class labels and check that it is a binary classification
# problem
label_encoder = LabelEncoder()
self.y_train_ = label_encoder.fit_transform(y)
self.classes_ = label_encoder.classes_
if self.classes_.size > 2:
raise ValueError("%s supports only binary classification. "
"y contains classes %s"
% (self.__class__.__name__, self.classes_))
elif self.classes_.size == 1:
raise ValueError("{0:s} requires 2 classes; got {1:d} class"
.format(self.__class__.__name__,
self.classes_.size))
if self.optimizer is not None and self.kernel_.n_dims > 0:
# Choose hyperparameters based on maximizing the log-marginal
# likelihood (potentially starting from several initial values)
def obj_func(theta, eval_gradient=True):
if eval_gradient:
lml, grad = self.log_marginal_likelihood(
theta, eval_gradient=True, clone_kernel=False)
return -lml, -grad
else:
return -self.log_marginal_likelihood(theta,
clone_kernel=False)
# First optimize starting from theta specified in kernel
optima = [self._constrained_optimization(obj_func,
self.kernel_.theta,
self.kernel_.bounds)]
# Additional runs are performed from log-uniform chosen initial
# theta
if self.n_restarts_optimizer > 0:
if not np.isfinite(self.kernel_.bounds).all():
raise ValueError(
"Multiple optimizer restarts (n_restarts_optimizer>0) "
"requires that all bounds are finite.")
bounds = self.kernel_.bounds
for iteration in range(self.n_restarts_optimizer):
theta_initial = np.exp(self.rng.uniform(bounds[:, 0],
bounds[:, 1]))
optima.append(
self._constrained_optimization(obj_func, theta_initial,
bounds))
# Select result from run with minimal (negative) log-marginal
# likelihood
lml_values = list(map(itemgetter(1), optima))
self.kernel_.theta = optima[np.argmin(lml_values)][0]
self.log_marginal_likelihood_value_ = -np.min(lml_values)
else:
self.log_marginal_likelihood_value_ = \
self.log_marginal_likelihood(self.kernel_.theta)
# Precompute quantities required for predictions which are independent
# of actual query points
K = self.kernel_(self.X_train_)
_, (self.pi_, self.W_sr_, self.L_, _, _) = \
self._posterior_mode(K, return_temporaries=True)
return self
def predict(self, X):
"""Perform classification on an array of test vectors X.
Parameters
----------
X : array-like of shape (n_samples, n_features) or list of object
Query points where the GP is evaluated for classification.
Returns
-------
C : ndarray of shape (n_samples,)
Predicted target values for X, values are from ``classes_``
"""
check_is_fitted(self)
# As discussed on Section 3.4.2 of GPML, for making hard binary
# decisions, it is enough to compute the MAP of the posterior and
# pass it through the link function
K_star = self.kernel_(self.X_train_, X) # K_star =k(x_star)
f_star = K_star.T.dot(self.y_train_ - self.pi_) # Algorithm 3.2,Line 4
return np.where(f_star > 0, self.classes_[1], self.classes_[0])
def predict_proba(self, X):
"""Return probability estimates for the test vector X.
Parameters
----------
X : array-like of shape (n_samples, n_features) or list of object
Query points where the GP is evaluated for classification.
Returns
-------
C : array-like of shape (n_samples, n_classes)
Returns the probability of the samples for each class in
the model. The columns correspond to the classes in sorted
order, as they appear in the attribute ``classes_``.
"""
check_is_fitted(self)
# Based on Algorithm 3.2 of GPML
K_star = self.kernel_(self.X_train_, X) # K_star =k(x_star)
f_star = K_star.T.dot(self.y_train_ - self.pi_) # Line 4
v = solve(self.L_, self.W_sr_[:, np.newaxis] * K_star) # Line 5
# Line 6 (compute np.diag(v.T.dot(v)) via einsum)
var_f_star = self.kernel_.diag(X) - np.einsum("ij,ij->j", v, v)
# Line 7:
# Approximate \int log(z) * N(z | f_star, var_f_star)
# Approximation is due to Williams & Barber, "Bayesian Classification
# with Gaussian Processes", Appendix A: Approximate the logistic
# sigmoid by a linear combination of 5 error functions.
# For information on how this integral can be computed see
# blitiri.blogspot.de/2012/11/gaussian-integral-of-error-function.html
alpha = 1 / (2 * var_f_star)
gamma = LAMBDAS * f_star
integrals = np.sqrt(np.pi / alpha) \
* erf(gamma * np.sqrt(alpha / (alpha + LAMBDAS**2))) \
/ (2 * np.sqrt(var_f_star * 2 * np.pi))
pi_star = (COEFS * integrals).sum(axis=0) + .5 * COEFS.sum()
return np.vstack((1 - pi_star, pi_star)).T
def log_marginal_likelihood(self, theta=None, eval_gradient=False,
clone_kernel=True):
"""Returns log-marginal likelihood of theta for training data.
Parameters
----------
theta : array-like of shape (n_kernel_params,), default=None
Kernel hyperparameters for which the log-marginal likelihood is
evaluated. If None, the precomputed log_marginal_likelihood
of ``self.kernel_.theta`` is returned.
eval_gradient : bool, default=False
If True, the gradient of the log-marginal likelihood with respect
to the kernel hyperparameters at position theta is returned
additionally. If True, theta must not be None.
clone_kernel : bool, default=True
If True, the kernel attribute is copied. If False, the kernel
attribute is modified, but may result in a performance improvement.
Returns
-------
log_likelihood : float
Log-marginal likelihood of theta for training data.
log_likelihood_gradient : ndarray of shape (n_kernel_params,), \
optional
Gradient of the log-marginal likelihood with respect to the kernel
hyperparameters at position theta.
Only returned when `eval_gradient` is True.
"""
if theta is None:
if eval_gradient:
raise ValueError(
"Gradient can only be evaluated for theta!=None")
return self.log_marginal_likelihood_value_
if clone_kernel:
kernel = self.kernel_.clone_with_theta(theta)
else:
kernel = self.kernel_
kernel.theta = theta
if eval_gradient:
K, K_gradient = kernel(self.X_train_, eval_gradient=True)
else:
K = kernel(self.X_train_)
# Compute log-marginal-likelihood Z and also store some temporaries
# which can be reused for computing Z's gradient
Z, (pi, W_sr, L, b, a) = \
self._posterior_mode(K, return_temporaries=True)
if not eval_gradient:
return Z
# Compute gradient based on Algorithm 5.1 of GPML
d_Z = np.empty(theta.shape[0])
# XXX: Get rid of the np.diag() in the next line
R = W_sr[:, np.newaxis] * cho_solve((L, True), np.diag(W_sr)) # Line 7
C = solve(L, W_sr[:, np.newaxis] * K) # Line 8
# Line 9: (use einsum to compute np.diag(C.T.dot(C))))
s_2 = -0.5 * (np.diag(K) - np.einsum('ij, ij -> j', C, C)) \
* (pi * (1 - pi) * (1 - 2 * pi)) # third derivative
for j in range(d_Z.shape[0]):
C = K_gradient[:, :, j] # Line 11
# Line 12: (R.T.ravel().dot(C.ravel()) = np.trace(R.dot(C)))
s_1 = .5 * a.T.dot(C).dot(a) - .5 * R.T.ravel().dot(C.ravel())
b = C.dot(self.y_train_ - pi) # Line 13
s_3 = b - K.dot(R.dot(b)) # Line 14
d_Z[j] = s_1 + s_2.T.dot(s_3) # Line 15
return Z, d_Z
def _posterior_mode(self, K, return_temporaries=False):
"""Mode-finding for binary Laplace GPC and fixed kernel.
This approximates the posterior of the latent function values for given
inputs and target observations with a Gaussian approximation and uses
Newton's iteration to find the mode of this approximation.
"""
# Based on Algorithm 3.1 of GPML
# If warm_start are enabled, we reuse the last solution for the
# posterior mode as initialization; otherwise, we initialize with 0
if self.warm_start and hasattr(self, "f_cached") \
and self.f_cached.shape == self.y_train_.shape:
f = self.f_cached
else:
f = np.zeros_like(self.y_train_, dtype=np.float64)
# Use Newton's iteration method to find mode of Laplace approximation
log_marginal_likelihood = -np.inf
for _ in range(self.max_iter_predict):
# Line 4
pi = expit(f)
W = pi * (1 - pi)
# Line 5
W_sr = np.sqrt(W)
W_sr_K = W_sr[:, np.newaxis] * K
B = np.eye(W.shape[0]) + W_sr_K * W_sr
L = cholesky(B, lower=True)
# Line 6
b = W * f + (self.y_train_ - pi)
# Line 7
a = b - W_sr * cho_solve((L, True), W_sr_K.dot(b))
# Line 8
f = K.dot(a)
# Line 10: Compute log marginal likelihood in loop and use as
# convergence criterion
lml = -0.5 * a.T.dot(f) \
- np.log1p(np.exp(-(self.y_train_ * 2 - 1) * f)).sum() \
- np.log(np.diag(L)).sum()
# Check if we have converged (log marginal likelihood does
# not decrease)
# XXX: more complex convergence criterion
if lml - log_marginal_likelihood < 1e-10:
break
log_marginal_likelihood = lml
self.f_cached = f # Remember solution for later warm-starts
if return_temporaries:
return log_marginal_likelihood, (pi, W_sr, L, b, a)
else:
return log_marginal_likelihood
def _constrained_optimization(self, obj_func, initial_theta, bounds):
if self.optimizer == "fmin_l_bfgs_b":
opt_res = scipy.optimize.minimize(
obj_func, initial_theta, method="L-BFGS-B", jac=True,
bounds=bounds)
_check_optimize_result("lbfgs", opt_res)
theta_opt, func_min = opt_res.x, opt_res.fun
elif callable(self.optimizer):
theta_opt, func_min = \
self.optimizer(obj_func, initial_theta, bounds=bounds)
else:
raise ValueError("Unknown optimizer %s." % self.optimizer)
return theta_opt, func_min
class GaussianProcessClassifier(ClassifierMixin, BaseEstimator):
"""Gaussian process classification (GPC) based on Laplace approximation.
The implementation is based on Algorithm 3.1, 3.2, and 5.1 of
Gaussian Processes for Machine Learning (GPML) by Rasmussen and
Williams.
Internally, the Laplace approximation is used for approximating the
non-Gaussian posterior by a Gaussian.
Currently, the implementation is restricted to using the logistic link
function. For multi-class classification, several binary one-versus rest
classifiers are fitted. Note that this class thus does not implement
a true multi-class Laplace approximation.
Read more in the :ref:`User Guide <gaussian_process>`.
Parameters
----------
kernel : kernel instance, default=None
The kernel specifying the covariance function of the GP. If None is
passed, the kernel "1.0 * RBF(1.0)" is used as default. Note that
the kernel's hyperparameters are optimized during fitting.
optimizer : 'fmin_l_bfgs_b' or callable, default='fmin_l_bfgs_b'
Can either be one of the internally supported optimizers for optimizing
the kernel's parameters, specified by a string, or an externally
defined optimizer passed as a callable. If a callable is passed, it
must have the signature::
def optimizer(obj_func, initial_theta, bounds):
# * 'obj_func' is the objective function to be maximized, which
# takes the hyperparameters theta as parameter and an
# optional flag eval_gradient, which determines if the
# gradient is returned additionally to the function value
# * 'initial_theta': the initial value for theta, which can be
# used by local optimizers
# * 'bounds': the bounds on the values of theta
....
# Returned are the best found hyperparameters theta and
# the corresponding value of the target function.
return theta_opt, func_min
Per default, the 'L-BFGS-B' algorithm from scipy.optimize.minimize
is used. If None is passed, the kernel's parameters are kept fixed.
Available internal optimizers are::
'fmin_l_bfgs_b'
n_restarts_optimizer : int, default=0
The number of restarts of the optimizer for finding the kernel's
parameters which maximize the log-marginal likelihood. The first run
of the optimizer is performed from the kernel's initial parameters,
the remaining ones (if any) from thetas sampled log-uniform randomly
from the space of allowed theta-values. If greater than 0, all bounds
must be finite. Note that n_restarts_optimizer=0 implies that one
run is performed.
max_iter_predict : int, default=100
The maximum number of iterations in Newton's method for approximating
the posterior during predict. Smaller values will reduce computation
time at the cost of worse results.
warm_start : bool, default=False
If warm-starts are enabled, the solution of the last Newton iteration
on the Laplace approximation of the posterior mode is used as
initialization for the next call of _posterior_mode(). This can speed
up convergence when _posterior_mode is called several times on similar
problems as in hyperparameter optimization. See :term:`the Glossary
<warm_start>`.
copy_X_train : bool, default=True
If True, a persistent copy of the training data is stored in the
object. Otherwise, just a reference to the training data is stored,
which might cause predictions to change if the data is modified
externally.
random_state : int or RandomState, default=None
Determines random number generation used to initialize the centers.
Pass an int for reproducible results across multiple function calls.
See :term: `Glossary <random_state>`.
multi_class : {'one_vs_rest', 'one_vs_one'}, default='one_vs_rest'
Specifies how multi-class classification problems are handled.
Supported are 'one_vs_rest' and 'one_vs_one'. In 'one_vs_rest',
one binary Gaussian process classifier is fitted for each class, which
is trained to separate this class from the rest. In 'one_vs_one', one
binary Gaussian process classifier is fitted for each pair of classes,
which is trained to separate these two classes. The predictions of
these binary predictors are combined into multi-class predictions.
Note that 'one_vs_one' does not support predicting probability
estimates.
n_jobs : int, default=None
The number of jobs to use for the computation.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
Attributes
----------
kernel_ : kernel instance
The kernel used for prediction. In case of binary classification,
the structure of the kernel is the same as the one passed as parameter
but with optimized hyperparameters. In case of multi-class
classification, a CompoundKernel is returned which consists of the
different kernels used in the one-versus-rest classifiers.
log_marginal_likelihood_value_ : float
The log-marginal-likelihood of ``self.kernel_.theta``
classes_ : array-like of shape (n_classes,)
Unique class labels.
n_classes_ : int
The number of classes in the training data
Examples
--------
>>> from sklearn.datasets import load_iris
>>> from sklearn.gaussian_process import GaussianProcessClassifier
>>> from sklearn.gaussian_process.kernels import RBF
>>> X, y = load_iris(return_X_y=True)
>>> kernel = 1.0 * RBF(1.0)
>>> gpc = GaussianProcessClassifier(kernel=kernel,
... random_state=0).fit(X, y)
>>> gpc.score(X, y)
0.9866...
>>> gpc.predict_proba(X[:2,:])
array([[0.83548752, 0.03228706, 0.13222543],
[0.79064206, 0.06525643, 0.14410151]])
.. versionadded:: 0.18
"""
@_deprecate_positional_args
def __init__(self, kernel=None, *, optimizer="fmin_l_bfgs_b",
n_restarts_optimizer=0, max_iter_predict=100,
warm_start=False, copy_X_train=True, random_state=None,
multi_class="one_vs_rest", n_jobs=None):
self.kernel = kernel
self.optimizer = optimizer
self.n_restarts_optimizer = n_restarts_optimizer
self.max_iter_predict = max_iter_predict
self.warm_start = warm_start
self.copy_X_train = copy_X_train
self.random_state = random_state
self.multi_class = multi_class
self.n_jobs = n_jobs
def fit(self, X, y):
"""Fit Gaussian process classification model
Parameters
----------
X : array-like of shape (n_samples, n_features) or list of object
Feature vectors or other representations of training data.
y : array-like of shape (n_samples,)
Target values, must be binary
Returns
-------
self : returns an instance of self.
"""
if self.kernel is None or self.kernel.requires_vector_input:
X, y = self._validate_data(X, y, multi_output=False,
ensure_2d=True, dtype="numeric")
else:
X, y = self._validate_data(X, y, multi_output=False,
ensure_2d=False, dtype=None)
self.base_estimator_ = _BinaryGaussianProcessClassifierLaplace(
kernel=self.kernel,
optimizer=self.optimizer,
n_restarts_optimizer=self.n_restarts_optimizer,
max_iter_predict=self.max_iter_predict,
warm_start=self.warm_start,
copy_X_train=self.copy_X_train,
random_state=self.random_state)
self.classes_ = np.unique(y)
self.n_classes_ = self.classes_.size
if self.n_classes_ == 1:
raise ValueError("GaussianProcessClassifier requires 2 or more "
"distinct classes; got %d class (only class %s "
"is present)"
% (self.n_classes_, self.classes_[0]))
if self.n_classes_ > 2:
if self.multi_class == "one_vs_rest":
self.base_estimator_ = \
OneVsRestClassifier(self.base_estimator_,
n_jobs=self.n_jobs)
elif self.multi_class == "one_vs_one":
self.base_estimator_ = \
OneVsOneClassifier(self.base_estimator_,
n_jobs=self.n_jobs)
else:
raise ValueError("Unknown multi-class mode %s"
% self.multi_class)
self.base_estimator_.fit(X, y)
if self.n_classes_ > 2:
self.log_marginal_likelihood_value_ = np.mean(
[estimator.log_marginal_likelihood()
for estimator in self.base_estimator_.estimators_])
else:
self.log_marginal_likelihood_value_ = \
self.base_estimator_.log_marginal_likelihood()
return self
def predict(self, X):
"""Perform classification on an array of test vectors X.
Parameters
----------
X : array-like of shape (n_samples, n_features) or list of object
Query points where the GP is evaluated for classification.
Returns
-------
C : ndarray of shape (n_samples,)
Predicted target values for X, values are from ``classes_``
"""
check_is_fitted(self)
if self.kernel is None or self.kernel.requires_vector_input:
X = check_array(X, ensure_2d=True, dtype="numeric")
else:
X = check_array(X, ensure_2d=False, dtype=None)
return self.base_estimator_.predict(X)
def predict_proba(self, X):
"""Return probability estimates for the test vector X.
Parameters
----------
X : array-like of shape (n_samples, n_features) or list of object
Query points where the GP is evaluated for classification.
Returns
-------
C : array-like of shape (n_samples, n_classes)
Returns the probability of the samples for each class in
the model. The columns correspond to the classes in sorted
order, as they appear in the attribute :term:`classes_`.
"""
check_is_fitted(self)
if self.n_classes_ > 2 and self.multi_class == "one_vs_one":
raise ValueError("one_vs_one multi-class mode does not support "
"predicting probability estimates. Use "
"one_vs_rest mode instead.")
if self.kernel is None or self.kernel.requires_vector_input:
X = check_array(X, ensure_2d=True, dtype="numeric")
else:
X = check_array(X, ensure_2d=False, dtype=None)
return self.base_estimator_.predict_proba(X)
@property
def kernel_(self):
if self.n_classes_ == 2:
return self.base_estimator_.kernel_
else:
return CompoundKernel(
[estimator.kernel_
for estimator in self.base_estimator_.estimators_])
def log_marginal_likelihood(self, theta=None, eval_gradient=False,
clone_kernel=True):
"""Returns log-marginal likelihood of theta for training data.
In the case of multi-class classification, the mean log-marginal
likelihood of the one-versus-rest classifiers are returned.
Parameters
----------
theta : array-like of shape (n_kernel_params,), default=None
Kernel hyperparameters for which the log-marginal likelihood is
evaluated. In the case of multi-class classification, theta may
be the hyperparameters of the compound kernel or of an individual
kernel. In the latter case, all individual kernel get assigned the
same theta values. If None, the precomputed log_marginal_likelihood
of ``self.kernel_.theta`` is returned.
eval_gradient : bool, default=False
If True, the gradient of the log-marginal likelihood with respect
to the kernel hyperparameters at position theta is returned
additionally. Note that gradient computation is not supported
for non-binary classification. If True, theta must not be None.
clone_kernel : bool, default=True
If True, the kernel attribute is copied. If False, the kernel
attribute is modified, but may result in a performance improvement.
Returns
-------
log_likelihood : float
Log-marginal likelihood of theta for training data.
log_likelihood_gradient : ndarray of shape (n_kernel_params,), optional
Gradient of the log-marginal likelihood with respect to the kernel
hyperparameters at position theta.
Only returned when `eval_gradient` is True.
"""
check_is_fitted(self)
if theta is None:
if eval_gradient:
raise ValueError(
"Gradient can only be evaluated for theta!=None")
return self.log_marginal_likelihood_value_
theta = np.asarray(theta)
if self.n_classes_ == 2:
return self.base_estimator_.log_marginal_likelihood(
theta, eval_gradient, clone_kernel=clone_kernel)
else:
if eval_gradient:
raise NotImplementedError(
"Gradient of log-marginal-likelihood not implemented for "
"multi-class GPC.")
estimators = self.base_estimator_.estimators_
n_dims = estimators[0].kernel_.n_dims
if theta.shape[0] == n_dims: # use same theta for all sub-kernels
return np.mean(
[estimator.log_marginal_likelihood(
theta, clone_kernel=clone_kernel)
for i, estimator in enumerate(estimators)])
elif theta.shape[0] == n_dims * self.classes_.shape[0]:
# theta for compound kernel
return np.mean(
[estimator.log_marginal_likelihood(
theta[n_dims * i:n_dims * (i + 1)],
clone_kernel=clone_kernel)
for i, estimator in enumerate(estimators)])
else:
raise ValueError("Shape of theta must be either %d or %d. "
"Obtained theta with shape %d."
% (n_dims, n_dims * self.classes_.shape[0],
theta.shape[0]))