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Added some numerical stability to link functions with tests for link functions
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Alan Saul
parent
034d141d63
commit
5c9587404d
3 changed files with 197 additions and 27 deletions
143
GPy/testing/link_function_tests.py
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143
GPy/testing/link_function_tests.py
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import numpy as np
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import scipy as sp
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from scipy.special import cbrt
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from GPy.models import GradientChecker
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_lim_val = np.finfo(np.float64).max
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_lim_val_exp = np.log(_lim_val)
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_lim_val_square = np.sqrt(_lim_val)
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_lim_val_cube = cbrt(_lim_val)
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from GPy.likelihoods.link_functions import Identity, Probit, Cloglog, Log, Log_ex_1, Reciprocal, Heaviside
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class LinkFunctionTests(np.testing.TestCase):
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def setUp(self):
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self.small_f = np.array([[-1e-4]])
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self.zero_f = np.array([[1e-4]])
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self.mid_f = np.array([[5.0]])
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self.large_f = np.array([[1e4]])
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self.f_lower_lim = np.array(-np.inf)
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self.f_upper_lim = np.array(np.inf)
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def check_gradient(self, link_func, lim_of_inf, test_lim=False):
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grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=self.mid_f)
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self.assertTrue(grad.checkgrad(verbose=True))
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grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=self.mid_f)
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self.assertTrue(grad2.checkgrad(verbose=True))
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grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=self.mid_f)
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self.assertTrue(grad3.checkgrad(verbose=True))
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grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=self.small_f)
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self.assertTrue(grad.checkgrad(verbose=True))
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grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=self.small_f)
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self.assertTrue(grad2.checkgrad(verbose=True))
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grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=self.small_f)
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self.assertTrue(grad3.checkgrad(verbose=True))
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grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=self.zero_f)
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self.assertTrue(grad.checkgrad(verbose=True))
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grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=self.zero_f)
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self.assertTrue(grad2.checkgrad(verbose=True))
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grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=self.zero_f)
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self.assertTrue(grad3.checkgrad(verbose=True))
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#Do a limit test if the large f value is too large
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large_f = np.clip(self.large_f, -np.inf, lim_of_inf-1e-3)
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grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=large_f)
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self.assertTrue(grad.checkgrad(verbose=True))
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grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=large_f)
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self.assertTrue(grad2.checkgrad(verbose=True))
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grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=large_f)
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self.assertTrue(grad3.checkgrad(verbose=True))
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if test_lim:
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print "Testing limits"
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#Remove some otherwise we are too close to the limit for gradcheck to work effectively
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lim_of_inf = lim_of_inf - 1e-4
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grad = GradientChecker(link_func.transf, link_func.dtransf_df, x0=lim_of_inf)
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self.assertTrue(grad.checkgrad(verbose=True))
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grad2 = GradientChecker(link_func.dtransf_df, link_func.d2transf_df2, x0=lim_of_inf)
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self.assertTrue(grad2.checkgrad(verbose=True))
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grad3 = GradientChecker(link_func.d2transf_df2, link_func.d3transf_df3, x0=lim_of_inf)
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self.assertTrue(grad3.checkgrad(verbose=True))
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def check_overflow(self, link_func, lim_of_inf):
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#Check that it does something sensible beyond this limit,
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#note this is not checking the value is correct, just that it isn't nan
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beyond_lim_of_inf = lim_of_inf + 100.0
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self.assertFalse(np.isinf(link_func.transf(beyond_lim_of_inf)))
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self.assertFalse(np.isinf(link_func.dtransf_df(beyond_lim_of_inf)))
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self.assertFalse(np.isinf(link_func.d2transf_df2(beyond_lim_of_inf)))
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self.assertFalse(np.isnan(link_func.transf(beyond_lim_of_inf)))
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self.assertFalse(np.isnan(link_func.dtransf_df(beyond_lim_of_inf)))
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self.assertFalse(np.isnan(link_func.d2transf_df2(beyond_lim_of_inf)))
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def test_log_overflow(self):
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link = Log()
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lim_of_inf = _lim_val_exp
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np.testing.assert_almost_equal(np.exp(self.mid_f), link.transf(self.mid_f))
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assert np.isinf(np.exp(np.log(self.f_upper_lim)))
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#Check the clipping works
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np.testing.assert_almost_equal(link.transf(self.f_lower_lim), 0, decimal=5)
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#Need to look at most significant figures here rather than the decimals
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np.testing.assert_approx_equal(link.transf(self.f_upper_lim), _lim_val, significant=5)
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self.check_overflow(link, lim_of_inf)
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#Check that it would otherwise fail
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beyond_lim_of_inf = lim_of_inf + 10.0
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old_err_state = np.seterr(over='ignore')
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self.assertTrue(np.isinf(np.exp(beyond_lim_of_inf)))
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np.seterr(**old_err_state)
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def test_log_ex_1_overflow(self):
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link = Log_ex_1()
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lim_of_inf = _lim_val_exp
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np.testing.assert_almost_equal(np.log1p(np.exp(self.mid_f)), link.transf(self.mid_f))
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assert np.isinf(np.log1p(np.exp(np.log(self.f_upper_lim))))
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#Check the clipping works
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np.testing.assert_almost_equal(link.transf(self.f_lower_lim), 0, decimal=5)
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#Need to look at most significant figures here rather than the decimals
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np.testing.assert_approx_equal(link.transf(self.f_upper_lim), np.log1p(_lim_val), significant=5)
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self.check_overflow(link, lim_of_inf)
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#Check that it would otherwise fail
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beyond_lim_of_inf = lim_of_inf + 10.0
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old_err_state = np.seterr(over='ignore')
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self.assertTrue(np.isinf(np.log1p(np.exp(beyond_lim_of_inf))))
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np.seterr(**old_err_state)
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def test_log_gradients(self):
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# transf dtransf_df d2transf_df2 d3transf_df3
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link = Log()
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lim_of_inf = _lim_val_exp
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self.check_gradient(link, lim_of_inf, test_lim=True)
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def test_identity_gradients(self):
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link = Identity()
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lim_of_inf = _lim_val
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#FIXME: Should be able to think of a way to test the limits of this
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self.check_gradient(link, lim_of_inf, test_lim=False)
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def test_probit_gradients(self):
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link = Probit()
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lim_of_inf = _lim_val
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self.check_gradient(link, lim_of_inf, test_lim=True)
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def test_Cloglog_gradients(self):
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link = Cloglog()
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lim_of_inf = _lim_val_exp
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self.check_gradient(link, lim_of_inf, test_lim=True)
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def test_Log_ex_1_gradients(self):
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link = Log_ex_1()
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lim_of_inf = _lim_val_exp
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self.check_gradient(link, lim_of_inf, test_lim=True)
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self.check_overflow(link, lim_of_inf)
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def test_reciprocal_gradients(self):
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link = Reciprocal()
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lim_of_inf = _lim_val
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#Does not work with much smaller values, and values closer to zero than 1e-5
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self.check_gradient(link, lim_of_inf, test_lim=True)
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