def testIsotropicGaussianKernelHyperparameterLearning(self):
hyper = array([1.5, 1.1])
gkernel = SVGaussianKernel_iso(hyper)
# marginal likelihood and likelihood gradient
#
# in MATLAB:
# [nlml dnlml] = gpr(log([1.5, 1.1])', 'covSEiso',
# [.5, .1, .3; .9, 1.2, .1; .55, .234, .1; .234, .547, .675] ,
# [.5, 1, .5, 2]')
margl, marglderiv = marginalLikelihood(gkernel, self.X, self.Y, len(hyper), True)
self.assertAlmostEqual(margl, 7.514, 2)
for v, t in zip(marglderiv, [11.4659, -10.0714]):
self.assertAlmostEqual(v, t, 2)
# compare partial derivatives with result from Rasmussen's code
target0 = matrix('[0 .5543 .0321 .2018; .5543 0 .449 .4945; .0321 .449 0 .2527; .2018 .4945 .2527 0]')
target1 = matrix('[2.42 1.769 2.3877 2.2087; 1.769 2.42 1.914 1.8533; 2.3877 1.914 2.42 2.1519; 2.2087 1.8533 2.1519 2.42]')
pder0 = gkernel.derivative(self.X, 0)
pder1 = gkernel.derivative(self.X, 1)
for i, (target, pder) in enumerate([(target0, pder0), (target1, pder1)]):
for j in xrange(4):
self.assertAlmostEqual(target[i,j], pder[i,j], 2)
# optimize the marginal likelihood over the log hyperparameters
# using BFGS
argmin = optimize.fmin_bfgs(nlml, log(hyper), dnlml, args=[SVGaussianKernel_iso, self.X, self.Y], disp=False)
for d, t in zip(argmin, [-0.0893, 0.29]):
self.assertAlmostEqual(d, t, 2)
def testARDGaussianKernelHyperparameterLearning(self):
hyper = array([2., 2., .1])
# test derivatives
target0 = matrix('[0 .0046 .0001 0; .0046 0 .0268 0; .0001 .0268 0 0; 0 0 0 0]')
target1 = matrix('[0 .0345 .0006 0; .0345 0 .2044 0; .0006 .2044 0 0; 0 0 0 0]')
target2 = matrix('[0 .4561 .54 .012; .4561 0 0 0; .54 .0 0 0; .012 0 0 0]')
target3 = matrix('[2 .2281 .27 .0017; .2281 2 1.7528 0; .27 1.7528 2 0; .0017 0 0 2]')
pder0 = GaussianKernel_ard(hyper).derivative(self.X, 0)
pder1 = GaussianKernel_ard(hyper).derivative(self.X, 1)
pder2 = GaussianKernel_ard(hyper).derivative(self.X, 2)
# pder3 = GaussianKernel_ard(hyper).derivative(self.X, 3)
epsilon = .0001
for i, (target, pder) in enumerate([(target0, pder0), (target1, pder1), (target2, pder2)]):
for j in xrange(4):
for k in xrange(4):
if abs(target[j, k]-pder[j, k]) > epsilon:
print '\nelement [%d, %d] of pder%d differs from expected by > %f' % (j, k, i, epsilon)
print '\ntarget:'
print target
print '\npder:'
print pder
assert False
# marginal likelihood and likelihood gradient
gkernel = GaussianKernel_ard(hyper)
margl, marglderiv = marginalLikelihood(gkernel, self.X, self.Y, len(hyper), useCholesky=True)
self.assertAlmostEqual(margl, 5.8404, 2)
for d, t in zip(marglderiv, [0.0039, 0.0302, -0.1733, -1.8089]):
self.assertAlmostEqual(d, t, 2)
# make sure we're getting the same results for inversion and cholesky
imargl, imarglderiv = marginalLikelihood(gkernel, self.X, self.Y, len(hyper), useCholesky=False)
self.assertAlmostEqual(margl, imargl, 2)
for c, i in zip(marglderiv, imarglderiv):
self.assertAlmostEqual(c, i, 2)
# optimize the marginal likelihood over log hyperparameters using BFGS
hyper = array([2., 2., .1, 1.])
argmin = optimize.fmin_bfgs(nlml, log(hyper), dnlml, args=[SVGaussianKernel_ard, self.X, self.Y], disp=False)
for v, t in zip(argmin, [6.9714, 0.95405, -0.9769, 0.36469]):
self.assertAlmostEqual(v, t, 2)
def testMaternKernelHyperparameterLearning(self):
# we'll just confirm the likelihood & likelihood gradient, rather than
# all the intermediate steps. you can use the Gaussian kernel examples
# if you want to figure out the partial derivatives.
hyper = array([1.5, 1.1])
mkernel3 = MaternKernel3(hyper)
margl3, marglderiv3 = marginalLikelihood(mkernel3, self.X, self.Y, len(hyper))
self.assertAlmostEqual(margl3, 5.1827, 2)
self.assertAlmostEqual(marglderiv3[0], 1.6947897766, 2)
self.assertAlmostEqual(marglderiv3[1], -2.9350, 2)
def testMaternKernelHyperparameterLearning(self):
# we'll just confirm the likelihood & likelihood gradient, rather than
# all the intermediate steps. you can use the Gaussian kernel examples
# if you want to figure out the partial derivatives.
hyper = array([1.5, 1.1])
mkernel3 = MaternKernel3(hyper)
margl3, marglderiv3 = marginalLikelihood(mkernel3, self.X, self.Y,
len(hyper))
self.assertAlmostEqual(margl3, 5.1827, 2)
self.assertAlmostEqual(marglderiv3[0], 1.6947897766, 2)
self.assertAlmostEqual(marglderiv3[1], -2.9350, 2)
def testIsotropicGaussianKernelHyperparameterLearning(self):
hyper = array([1.5, 1.1])
gkernel = SVGaussianKernel_iso(hyper)
# marginal likelihood and likelihood gradient
#
# in MATLAB:
# [nlml dnlml] = gpr(log([1.5, 1.1])', 'covSEiso',
# [.5, .1, .3; .9, 1.2, .1; .55, .234, .1; .234, .547, .675] ,
# [.5, 1, .5, 2]')
margl, marglderiv = marginalLikelihood(gkernel, self.X, self.Y,
len(hyper), True)
self.assertAlmostEqual(margl, 7.514, 2)
for v, t in zip(marglderiv, [11.4659, -10.0714]):
self.assertAlmostEqual(v, t, 2)
# compare partial derivatives with result from Rasmussen's code
target0 = matrix(
'[0 .5543 .0321 .2018; .5543 0 .449 .4945; .0321 .449 0 .2527; .2018 .4945 .2527 0]'
)
target1 = matrix(
'[2.42 1.769 2.3877 2.2087; 1.769 2.42 1.914 1.8533; 2.3877 1.914 2.42 2.1519; 2.2087 1.8533 2.1519 2.42]'
)
pder0 = gkernel.derivative(self.X, 0)
pder1 = gkernel.derivative(self.X, 1)
for i, (target, pder) in enumerate([(target0, pder0),
(target1, pder1)]):
for j in xrange(4):
self.assertAlmostEqual(target[i, j], pder[i, j], 2)
# optimize the marginal likelihood over the log hyperparameters
# using BFGS
argmin = optimize.fmin_bfgs(
nlml,
log(hyper),
dnlml,
args=[SVGaussianKernel_iso, self.X, self.Y],
disp=False)
for d, t in zip(argmin, [-0.0893, 0.29]):
self.assertAlmostEqual(d, t, 2)
def testARDGaussianKernelHyperparameterLearning(self):
hyper = array([2., 2., .1])
# test derivatives
target0 = matrix(
'[0 .0046 .0001 0; .0046 0 .0268 0; .0001 .0268 0 0; 0 0 0 0]')
target1 = matrix(
'[0 .0345 .0006 0; .0345 0 .2044 0; .0006 .2044 0 0; 0 0 0 0]')
target2 = matrix(
'[0 .4561 .54 .012; .4561 0 0 0; .54 .0 0 0; .012 0 0 0]')
target3 = matrix(
'[2 .2281 .27 .0017; .2281 2 1.7528 0; .27 1.7528 2 0; .0017 0 0 2]'
)
pder0 = GaussianKernel_ard(hyper).derivative(self.X, 0)
pder1 = GaussianKernel_ard(hyper).derivative(self.X, 1)
pder2 = GaussianKernel_ard(hyper).derivative(self.X, 2)
# pder3 = GaussianKernel_ard(hyper).derivative(self.X, 3)
epsilon = .0001
for i, (target, pder) in enumerate([(target0, pder0), (target1, pder1),
(target2, pder2)]):
for j in xrange(4):
for k in xrange(4):
if abs(target[j, k] - pder[j, k]) > epsilon:
print '\nelement [%d, %d] of pder%d differs from expected by > %f' % (
j, k, i, epsilon)
print '\ntarget:'
print target
print '\npder:'
print pder
assert False
# marginal likelihood and likelihood gradient
gkernel = GaussianKernel_ard(hyper)
margl, marglderiv = marginalLikelihood(gkernel,
self.X,
self.Y,
len(hyper),
useCholesky=True)
self.assertAlmostEqual(margl, 5.8404, 2)
for d, t in zip(marglderiv, [0.0039, 0.0302, -0.1733, -1.8089]):
self.assertAlmostEqual(d, t, 2)
# make sure we're getting the same results for inversion and cholesky
imargl, imarglderiv = marginalLikelihood(gkernel,
self.X,
self.Y,
len(hyper),
useCholesky=False)
self.assertAlmostEqual(margl, imargl, 2)
for c, i in zip(marglderiv, imarglderiv):
self.assertAlmostEqual(c, i, 2)
# optimize the marginal likelihood over log hyperparameters using BFGS
hyper = array([2., 2., .1, 1.])
argmin = optimize.fmin_bfgs(
nlml,
log(hyper),
dnlml,
args=[SVGaussianKernel_ard, self.X, self.Y],
disp=False)
for v, t in zip(argmin, [6.9714, 0.95405, -0.9769, 0.36469]):
self.assertAlmostEqual(v, t, 2)
