code: def testNTKMeanCovPrediction(
      self,
      train_size,
      test_size,
      input_shape,
      out_logits,
  ):
      train_shape = (train_size, *input_shape)
      test_shape = (test_size, *input_shape)
      key, x_test, x_train, y_train = self._get_inputs(
          out_logits, test_shape, train_shape
      )
      init_fn, f, kernel_fn = stax.serial(
          stax.Dense(512, W_std=1.2, b_std=0.05),
          stax.Erf(),
          stax.Dense(out_logits, W_std=1.2, b_std=0.05),
      )
  
      reg = 1e-6
      predictor = predict.gradient_descent_mse_ensemble(
          kernel_fn, x_train, y_train, diag_reg=reg
      )
      ts = jnp.array([1.0, 5.0, 10.0])
  
      fx_test_inf, cov_test_inf = predictor(ts, x_test, "ntk", True)
      self.assertEqual(cov_test_inf.shape[1], x_test.shape[0])
      self.assertGreater(
          jnp.min(jnp.linalg.eigh(cov_test_inf)[0]), -1e-8
      )
  
      fx_train_inf, cov_train_inf = predictor(ts, None, "ntk", True)
      self.assertEqual(cov_train_inf.shape[1], x_train.shape[0])
      self.assertGreater(
          jnp.min(jnp.linalg.eigh(cov_train_inf)[0]), -1e-8
      )
  
      _kernel_fn = nt.empirical_kernel_fn(f)
      # TODO(romann): figure out the slow compile on Ubuntu 22.04 CPU Python 3.9
      kernel_fn = lambda x1, x2, params: _kernel_fn(
          x1, x2, "ntk", params
      )
  
      def predict_empirical(key):
          _, params = init_fn(key, train_shape)
          g_dd = kernel_fn(x_train, None, params)
          g_td = kernel_fn(x_test, x_train, params)
          predict_fn = predict.gradient_descent_mse(
              g_dd, y_train, diag_reg=reg
          )
          fx_train_0 = f(params, x_train)
          fx_test_0 = f(params, x_test)
          return predict_fn(ts, fx_train_0, fx_test_0, g_td)
  
      def predict_mc(count, key):
          key = random.split(key, count)
          fx_train, fx_test = vmap(predict_empirical)(key)
          fx_train_mean = jnp.mean(fx_train, axis=0, keepdims=True)
          fx_test_mean = jnp.mean(fx_test, axis=0, keepdims=True)
  
          fx_train_centered = fx_train - fx_train_mean
          fx_test_centered = fx_test - fx_test_mean
  
          cov_train = PredictTest._cov_empirical(fx_train_centered)
          cov_test = PredictTest._cov_empirical(fx_test_centered)
  
          return fx_train_mean, fx_test_mean, cov_train, cov_test
  
      fx_train_mc, fx_test_mc, cov_train_mc, cov_test_mc = predict_mc(
          4096, key
      )
      tol = 0.05
  
      assert_close = lambda a, b: self.assertAllClose(
          ravel_pytree(a)[0], ravel_pytree(b)[0], atol=tol, rtol=tol
      )
  
      assert_close(fx_train_mc, fx_train_inf)
      assert_close(cov_train_mc, cov_train_inf)
      assert_close(cov_test_mc, cov_test_inf)
      assert_close(fx_test_mc, fx_test_inf)
  
imports: import math
  from absl.testing import absltest
  from jax import grad
  from jax import jit
  from jax import random
  from jax import vmap
  from jax import config
  from jax.example_libraries import optimizers
  from jax.flatten_util import ravel_pytree
  import jax.numpy
  import jax.tree_util
  import neural_tangents
  from neural_tangents import predict, stax
  from neural_tangents._src.predict import _is_on_cpu
  from tests import test_utils
label_desc: Use image node_id 7 for calling the PredictTest obj's underlying member method code with example usage: obj.testNTKMeanCovPrediction(train_size, test_size, input_shape, out_logits) and returns: predict_fn, fx_train_mean,  fx_test_mean,  cov_train,  cov_test