8000 [MRG+1] Make return_std faster in Gaussian Processes by minghui-liu · Pull Request #9236 · scikit-learn/scikit-learn · GitHub
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[MRG+1] Make return_std faster in Gaussian Processes #9236

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[MRG+1] Make return_std faster in Gaussian Processes #9236

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6989c2b
Make return_std 20x faster in Gaussian Processes
minghui-liu Jun 27, 2017
02046de
make K_inv private attribute
minghui-liu Jun 28, 2017
44c7608
fix flake8 warnings
minghui-liu Jun 28, 2017
2b73508
delete _K_inv if L_ has changed
minghui-liu Jul 11, 2017
e57a1a8
test if self._K_inv is reset after new fit
minghui-liu Jul 13, 2017
f207b9f
update test_K_inv_reset()
minghui-liu Aug 2, 2017
630afab
Tweak comment
lesteve Aug 3, 2017
dd34652
Revert einsum optimization
Aug 13, 2017
2a37685
fix flake8 error
minghui-liu Aug 19, 2017
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17 changes: 12 additions & 5 deletions sklearn/gaussian_process/gpr.py
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Original file line number Diff line number Diff line change
Expand Up @@ -245,6 +245,8 @@ def obj_func(theta, eval_gradient=True):
K[np.diag_indices_from(K)] += self.alpha
try:
self.L_ = cholesky(K, lower=True) # Line 2
# self.L_ changed, self._K_inv needs to be recomputed
self._K_inv = None
except np.linalg.LinAlgError as exc:
exc.args = ("The kernel, %s, is not returning a "
"positive definite matrix. Try gradually "
Expand Down Expand Up @@ -320,13 +322,18 @@ def predict(self, X, return_std=False, return_cov=False):
y_cov = self.kernel_(X) - K_trans.dot(v) # Line 6
return y_mean, y_cov
elif return_std:
# compute inverse K_inv of K based on its Cholesky
# decomposition L and its inverse L_inv
L_inv = solve_triangular(self.L_.T, np.eye(self.L_.shape[0]))
K_inv = L_inv.dot(L_inv.T)
# cache result of K_inv computation
if self._K_inv is None:
# compute inverse K_inv of K based on its Cholesky
# decomposition L and its inverse L_inv
L_inv = solve_triangular(self.L_.T,
np.eye(self.L_.shape[0]))
self._K_inv = L_inv.dot(L_inv.T)
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self._K_inv needs to be deleted if self.L_ is changed during a second fit

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Hi. Thank you. How do I test if self.L_ has changed?

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self.L_ is changed only in this line, so you should add for example self._K_inv = Nonejust after, and change the condition to if self._K_inv is None

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Apologize for the delay. I've made the changes.


# Compute variance of predictive distribution
y_var = self.kernel_.diag(X)
y_var -= np.einsum("ij,ij->i", np.dot(K_trans, K_inv), K_trans)
y_var -= np.einsum("ij,ij->i",
np.dot(K_trans, self._K_inv), K_trans)

# Check if any of the variances is negative because of
# numerical issues. If yes: set the variance to 0.
Expand Down
22 changes: 21 additions & 1 deletion sklearn/gaussian_process/tests/test_gpr.py
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Expand Up @@ -15,11 +15,13 @@
from sklearn.utils.testing \
import (assert_true, assert_greater, assert_array_less,
assert_almost_equal, assert_equal, assert_raise_message,
assert_array_almost_equal)
assert_array_almost_equal, assert_array_equal)


def f(x):
return x * np.sin(x)


X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
X2 = np.atleast_2d([2., 4., 5.5, 6.5, 7.5]).T
y = f(X).ravel()
Expand Down Expand Up @@ -344,3 +346,21 @@ def test_no_fit_default_predict():

assert_array_almost_equal(y_std1, y_std2)
assert_array_almost_equal(y_cov1, y_cov2)


def test_K_inv_reset():
y2 = f(X2).ravel()
for kernel in kernels:
# Test that self._K_inv is reset after a new fit
gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
assert_true(hasattr(gpr, '_K_inv'))
assert_true(gpr._K_inv is None)
gpr.predict(X, return_std=True)
assert_true(gpr._K_inv is not None)
gpr.fit(X2, y2)
assert_true(gpr._K_inv is None)
gpr.predict(X2, return_std=True)
gpr2 = GaussianProcessRegressor(kernel=kernel).fit(X2, y2)
gpr2.predict(X2, return_std=True)
# the value of K_inv should be independent of the first fit
assert_array_equal(gpr._K_inv, gpr2._K_inv)
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