# Copyright 2018 Google LLC # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # https://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """Tests for nngp.py.""" from __future__ import absolute_import from __future__ import division from __future__ import print_function import numpy as np import tensorflow as tf import nngp class NNGPTest(tf.test.TestCase): def ExactQabArcCos(self, var_aa, corr_ab): """Exact integration result from Cho & Saul (2009). Specifically: qaa = 0.5*qaa qab = (qaa/2*pi)*(sin angle + (pi-angle)*cos angle), where cos angle = corr_ab. Args: var_aa: 1d tensor of variance grid points. corr_ab: 1d tensor of correlation grid points. Returns: qab_exact: tensor, exact covariance matrix. """ angle = tf.acos(corr_ab) jtheta = tf.sin(angle) + (np.pi - angle) * tf.cos(angle) term1 = tf.tile(tf.expand_dims(var_aa, 1), [1, corr_ab.shape[0]]) term2 = tf.tile(tf.expand_dims(jtheta, 0), [var_aa.shape[0], 1]) qab_exact = (1 / (2 * np.pi)) * term1 * term2 return qab_exact def testComputeQmapGridRelu(self): """Test checks the compute_qmap_grid function. (i) Checks sizes are appropriate and (ii) checks accuracy of the numerical values generated by the grid by comparing against the analytically known form for Relu (Cho and Saul, '09). """ n_gauss, n_var, n_corr = 301, 33, 31 kernel = nngp.NNGPKernel( nonlin_fn=tf.nn.relu, n_gauss=n_gauss, n_var=n_var, n_corr=n_corr) var_aa_grid = kernel.var_aa_grid corr_ab_grid = kernel.corr_ab_grid qaa_grid = kernel.qaa_grid qab_grid = kernel.qab_grid qaa_exact = 0.5 * var_aa_grid qab_exact = self.ExactQabArcCos(var_aa_grid, corr_ab_grid) with self.test_session() as sess: self.assertEqual(var_aa_grid.shape.as_list(), [n_var]) self.assertEqual(corr_ab_grid.shape.as_list(), [n_corr]) self.assertAllClose(sess.run(qaa_exact), sess.run(qaa_grid), rtol=1e-6) self.assertAllClose( sess.run(qab_exact), sess.run(qab_grid), rtol=1e-6, atol=2e-2) def testComputeQmapGridReluLogSpacing(self): n_gauss, n_var, n_corr = 301, 33, 31 kernel = nngp.NNGPKernel( nonlin_fn=tf.nn.relu, n_gauss=n_gauss, n_var=n_var, n_corr=n_corr) var_aa_grid = kernel.var_aa_grid corr_ab_grid = kernel.corr_ab_grid qaa_grid = kernel.qaa_grid qab_grid = kernel.qab_grid qaa_exact = 0.5 * var_aa_grid qab_exact = self.ExactQabArcCos(var_aa_grid, corr_ab_grid) with self.test_session() as sess: self.assertEqual(var_aa_grid.shape.as_list(), [n_var]) self.assertEqual(corr_ab_grid.shape.as_list(), [n_corr]) self.assertAllClose( sess.run(qaa_exact), sess.run(qaa_grid), rtol=1e-6, atol=2e-2) self.assertAllClose( sess.run(qab_exact), sess.run(qab_grid), rtol=1e-6, atol=2e-2) def testComputeQmapGridEvenNGauss(self): n_gauss, n_var, n_corr = 102, 33, 31 with self.assertRaises(ValueError): nngp.NNGPKernel( nonlin_fn=tf.nn.relu, n_gauss=n_gauss, n_var=n_var, n_corr=n_corr) def testGetVarFixedPoint(self): n_gauss, n_var, n_corr = 101, 33, 31 weight_var, bias_var = 1.9, 0.2 analytic_fixed_point = bias_var / (1. - weight_var/2) kernel = nngp.NNGPKernel( nonlin_fn=tf.nn.relu, weight_var=weight_var, bias_var=bias_var, n_gauss=n_gauss, n_var=n_var, n_corr=n_corr) fixed_point, _ = kernel.get_var_fixed_point() self.assertAllClose(analytic_fixed_point, fixed_point[0], atol=1e-4) if __name__ == "__main__": tf.test.main()