import numpy as np
import scipy
from scipy.special import cbrt
from GPy.models import GradientChecker
import random
_lim_val = np.finfo(np.float64).max
_lim_val_exp = np.log(_lim_val)
_lim_val_square = np.sqrt(_lim_val)
_lim_val_cube = cbrt(_lim_val)
from GPy.likelihoods.link_functions import Identity, Probit, Cloglog, Log, Log_ex_1, Reciprocal, Heaviside, ScaledProbit
[docs]class LinkFunctionTests(np.testing.TestCase):
[docs] def setUp(self):
self.small_f = np.array([[-1e-4]])
self.zero_f = np.array([[1e-4]])
self.mid_f = np.array([[5.0]])
self.large_f = np.array([[1e4]])
self.f_lower_lim = np.array(-np.inf)
self.f_upper_lim = np.array(np.inf)
[docs] def check_gradient(self, link_func, lim_of_inf, test_lim=False):
grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=self.mid_f)
self.assertTrue(grad.checkgrad(verbose=True))
grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=self.mid_f)
self.assertTrue(grad2.checkgrad(verbose=True))
grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=self.mid_f)
self.assertTrue(grad3.checkgrad(verbose=True))
grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=self.small_f)
self.assertTrue(grad.checkgrad(verbose=True))
grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=self.small_f)
self.assertTrue(grad2.checkgrad(verbose=True))
grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=self.small_f)
self.assertTrue(grad3.checkgrad(verbose=True))
grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=self.zero_f)
self.assertTrue(grad.checkgrad(verbose=True))
grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=self.zero_f)
self.assertTrue(grad2.checkgrad(verbose=True))
grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=self.zero_f)
self.assertTrue(grad3.checkgrad(verbose=True))
#Do a limit test if the large f value is too large
large_f = np.clip(self.large_f, -np.inf, lim_of_inf-1e-3)
grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=large_f)
self.assertTrue(grad.checkgrad(verbose=True))
grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=large_f)
self.assertTrue(grad2.checkgrad(verbose=True))
grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=large_f)
self.assertTrue(grad3.checkgrad(verbose=True))
if test_lim:
print("Testing limits")
#Remove some otherwise we are too close to the limit for gradcheck to work effectively
lim_of_inf = lim_of_inf - 1e-4
grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=lim_of_inf)
self.assertTrue(grad.checkgrad(verbose=True))
grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=lim_of_inf)
self.assertTrue(grad2.checkgrad(verbose=True))
grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=lim_of_inf)
self.assertTrue(grad3.checkgrad(verbose=True))
[docs] def check_overflow(self, link_func, lim_of_inf):
#Check that it does something sensible beyond this limit,
#note this is not checking the value is correct, just that it isn't nan
beyond_lim_of_inf = lim_of_inf + 100.0
self.assertFalse(np.isinf(link_func.transf(beyond_lim_of_inf)))
self.assertFalse(np.isinf(link_func.dtransf_df(beyond_lim_of_inf)))
self.assertFalse(np.isinf(link_func.d2transf_df2(beyond_lim_of_inf)))
self.assertFalse(np.isnan(link_func.transf(beyond_lim_of_inf)))
self.assertFalse(np.isnan(link_func.dtransf_df(beyond_lim_of_inf)))
self.assertFalse(np.isnan(link_func.d2transf_df2(beyond_lim_of_inf)))
[docs] def test_log_overflow(self):
link = Log()
lim_of_inf = _lim_val_exp
np.testing.assert_almost_equal(np.exp(self.mid_f), link.transf(self.mid_f))
assert np.isinf(np.exp(np.log(self.f_upper_lim)))
#Check the clipping works
np.testing.assert_almost_equal(link.transf(self.f_lower_lim), 0, decimal=5)
self.assertTrue(np.isfinite(link.transf(self.f_upper_lim)))
self.check_overflow(link, lim_of_inf)
#Check that it would otherwise fail
beyond_lim_of_inf = lim_of_inf + 10.0
old_err_state = np.seterr(over='ignore')
self.assertTrue(np.isinf(np.exp(beyond_lim_of_inf)))
np.seterr(**old_err_state)
[docs] def test_log_ex_1_overflow(self):
link = Log_ex_1()
lim_of_inf = _lim_val_exp
np.testing.assert_almost_equal(scipy.special.log1p(np.exp(self.mid_f)), link.transf(self.mid_f))
assert np.isinf(scipy.special.log1p(np.exp(np.log(self.f_upper_lim))))
#Check the clipping works
np.testing.assert_almost_equal(link.transf(self.f_lower_lim), 0, decimal=5)
#Need to look at most significant figures here rather than the decimals
np.testing.assert_approx_equal(link.transf(self.f_upper_lim), scipy.special.log1p(_lim_val), significant=5)
self.check_overflow(link, lim_of_inf)
#Check that it would otherwise fail
beyond_lim_of_inf = lim_of_inf + 10.0
old_err_state = np.seterr(over='ignore')
self.assertTrue(np.isinf(scipy.special.log1p(np.exp(beyond_lim_of_inf))))
np.seterr(**old_err_state)
[docs] def test_log_gradients(self):
# transf dtransf_df d2transf_df2 d3transf_df3
link = Log()
lim_of_inf = _lim_val_exp
self.check_gradient(link, lim_of_inf, test_lim=True)
[docs] def test_identity_gradients(self):
link = Identity()
lim_of_inf = _lim_val
#FIXME: Should be able to think of a way to test the limits of this
self.check_gradient(link, lim_of_inf, test_lim=False)
[docs] def test_probit_gradients(self):
link = Probit()
lim_of_inf = _lim_val
self.check_gradient(link, lim_of_inf, test_lim=True)
[docs] def test_scaledprobit_gradients(self):
link = ScaledProbit(nu=random.random())
lim_of_inf = _lim_val
self.check_gradient(link, lim_of_inf, test_lim=True)
[docs] def test_Cloglog_gradients(self):
link = Cloglog()
lim_of_inf = _lim_val_exp
self.check_gradient(link, lim_of_inf, test_lim=True)
[docs] def test_Log_ex_1_gradients(self):
link = Log_ex_1()
lim_of_inf = _lim_val_exp
self.check_gradient(link, lim_of_inf, test_lim=True)
self.check_overflow(link, lim_of_inf)
[docs] def test_reciprocal_gradients(self):
link = Reciprocal()
lim_of_inf = _lim_val
#Does not work with much smaller values, and values closer to zero than 1e-5
self.check_gradient(link, lim_of_inf, test_lim=True)