def test_simple_regression_correctness(self): # Verify that optimizing a simple linear regression by gradient descent # recovers the known-correct weights. batch_shape = [4, 3] num_timesteps = 10 num_features = 2 design_matrix = self._build_placeholder( np.random.randn(*(batch_shape + [num_timesteps, num_features]))) true_weights = self._build_placeholder([4., -3.]) predicted_time_series = linear_operator_util.matmul_with_broadcast( design_matrix, true_weights[..., tf.newaxis]) linear_regression = LinearRegression( design_matrix=design_matrix, weights_prior=tfd.Independent(tfd.Cauchy( loc=self._build_placeholder(np.zeros([num_features])), scale=self._build_placeholder(np.ones([num_features]))), reinterpreted_batch_ndims=1)) observation_noise_scale_prior = tfd.LogNormal( loc=self._build_placeholder(-2), scale=self._build_placeholder(0.1)) model = Sum( components=[linear_regression], observation_noise_scale_prior=observation_noise_scale_prior) learnable_weights = tf.Variable( tf.zeros([num_features], dtype=true_weights.dtype)) learnable_ssm = model.make_state_space_model( num_timesteps=num_timesteps, param_vals={ "LinearRegression/_weights": learnable_weights, "observation_noise_scale": observation_noise_scale_prior.mode() }) loss = -learnable_ssm.log_prob(predicted_time_series) train_op = tf.train.AdamOptimizer(0.1).minimize(loss) with self.test_session() as sess: sess.run(tf.global_variables_initializer()) for _ in range(80): _ = sess.run(train_op) self.assertAllClose(*sess.run((true_weights, learnable_weights)), atol=0.2)
def test_broadcast_batch_shapes(self): seed = test_util.test_seed(sampler_type='stateless') batch_shape = [3, 1, 4] partial_batch_shape = [2, 1] expected_broadcast_batch_shape = [3, 2, 4] # Build a model where parameters have different batch shapes. partial_batch_loc = self._build_placeholder( np.random.randn(*partial_batch_shape)) full_batch_loc = self._build_placeholder( np.random.randn(*batch_shape)) partial_scale_prior = tfd.LogNormal( loc=partial_batch_loc, scale=tf.ones_like(partial_batch_loc)) full_scale_prior = tfd.LogNormal( loc=full_batch_loc, scale=tf.ones_like(full_batch_loc)) loc_prior = tfd.Normal(loc=partial_batch_loc, scale=tf.ones_like(partial_batch_loc)) linear_trend = LocalLinearTrend(level_scale_prior=full_scale_prior, slope_scale_prior=full_scale_prior, initial_level_prior=loc_prior, initial_slope_prior=loc_prior) seasonal = Seasonal(num_seasons=3, drift_scale_prior=partial_scale_prior, initial_effect_prior=loc_prior) model = Sum([linear_trend, seasonal], observation_noise_scale_prior=partial_scale_prior) param_samples = [p.prior.sample(seed=seed) for p in model.parameters] ssm = model.make_state_space_model(num_timesteps=2, param_vals=param_samples) # Test that the model's batch shape matches the SSM's batch shape, # and that they both match the expected broadcast shape. self.assertAllEqual(model.batch_shape, ssm.batch_shape) (model_batch_shape_tensor_, ssm_batch_shape_tensor_) = self.evaluate((model.batch_shape_tensor(), ssm.batch_shape_tensor())) self.assertAllEqual(model_batch_shape_tensor_, ssm_batch_shape_tensor_) self.assertAllEqual(model_batch_shape_tensor_, expected_broadcast_batch_shape)
def test_broadcast_batch_shapes(self): batch_shape = [3, 1, 4] partial_batch_shape = [2, 1] expected_broadcast_batch_shape = [3, 2, 4] # Build a model where parameters have different batch shapes. partial_batch_loc = self._build_placeholder( np.random.randn(*partial_batch_shape)) full_batch_loc = self._build_placeholder( np.random.randn(*batch_shape)) partial_scale_prior = tfd.LogNormal( loc=partial_batch_loc, scale=tf.ones_like(partial_batch_loc)) full_scale_prior = tfd.LogNormal( loc=full_batch_loc, scale=tf.ones_like(full_batch_loc)) loc_prior = tfd.Normal(loc=partial_batch_loc, scale=tf.ones_like(partial_batch_loc)) linear_trend = LocalLinearTrend(level_scale_prior=full_scale_prior, slope_scale_prior=full_scale_prior, initial_level_prior=loc_prior, initial_slope_prior=loc_prior) seasonal = Seasonal(num_seasons=3, drift_scale_prior=partial_scale_prior, initial_effect_prior=loc_prior) model = Sum([linear_trend, seasonal], observation_noise_scale_prior=partial_scale_prior) param_samples = [p.prior.sample() for p in model.parameters] ssm = model.make_state_space_model(num_timesteps=2, param_vals=param_samples) # Test that the model's batch shape matches the SSM's batch shape, # and that they both match the expected broadcast shape. self.assertAllEqual(model.batch_shape, ssm.batch_shape) (model_batch_shape_tensor_, ssm_batch_shape_tensor_) = self.evaluate((model.batch_shape_tensor(), ssm.batch_shape_tensor())) self.assertAllEqual(model_batch_shape_tensor_, ssm_batch_shape_tensor_) self.assertAllEqual(model_batch_shape_tensor_, expected_broadcast_batch_shape)