code: def testGpInference(self):
      reg = 1e-5
      key = random.PRNGKey(1)
      x_train = random.normal(key, (4, 2))
      init_fn, apply_fn, kernel_fn_analytic = stax.serial(
          stax.Dense(32, 2.0, 0.5),
          stax.Relu(),
          stax.Dense(10, 2.0, 0.5),
      )
      kernel_fn_empirical = nt.empirical_kernel_fn(apply_fn)
      y_train = random.normal(key, (4, 10))
      for kernel_fn_is_analytic in [True, False]:
          if kernel_fn_is_analytic:
              kernel_fn = kernel_fn_analytic
          else:
              _, params = init_fn(key, x_train.shape)
  
              def kernel_fn(x1, x2, get):
                  return kernel_fn_empirical(x1, x2, get, params)
  
          for get in [
              None,
              "nngp",
              "ntk",
              ("nngp",),
              ("ntk",),
              ("nngp", "ntk"),
              ("ntk", "nngp"),
          ]:
              k_dd = kernel_fn(x_train, None, get)
  
              gp_inference = predict.gp_inference(
                  k_dd, y_train, diag_reg=reg
              )
              gd_ensemble = predict.gradient_descent_mse_ensemble(
                  kernel_fn, x_train, y_train, diag_reg=reg
              )
              for x_test in [None, "x_test"]:
                  x_test = (
                      None
                      if x_test is None
                      else random.normal(key, (8, 2))
                  )
                  k_td = (
                      None
                      if x_test is None
                      else kernel_fn(x_test, x_train, get)
                  )
  
                  for compute_cov in [True, False]:
                      with self.subTest(
                          kernel_fn_is_analytic=kernel_fn_is_analytic,
                          get=get,
                          x_test=x_test if x_test is None else "x_test",
                          compute_cov=compute_cov,
                      ):
                          if compute_cov:
                              nngp_tt = (
                                  True
                                  if x_test is None
                                  else kernel_fn(x_test, None, "nngp")
                              )
                          else:
                              nngp_tt = None
  
                          out_ens = gd_ensemble(
                              None, x_test, get, compute_cov
                          )
                          out_ens_inf = gd_ensemble(
                              jnp.inf, x_test, get, compute_cov
                          )
                          tol = (
                              0.35
                              if jax.default_backend() == "tpu"
                              else 0.08
                          )
                          self.assertAllClose(
                              out_ens_inf, out_ens, rtol=tol, atol=tol
                          )
  
                          if (
                              get is not None
                              and "nngp" not in get
                              and compute_cov
                              and k_td is not None
                          ):
                              with self.assertRaises(ValueError):
                                  out_gp_inf = gp_inference(
                                      get=get,
                                      k_test_train=k_td,
                                      k_test_test=nngp_tt,
                                  )
                          else:
                              out_gp_inf = gp_inference(
                                  get=get,
                                  k_test_train=k_td,
                                  k_test_test=nngp_tt,
                              )
                              self.assertAllClose(out_ens, out_gp_inf)
  
          # Test NTKGP
          for get in [
              (),
              ("nngp",),
              ("ntk",),
              ("nngp", "ntk"),
              ("ntk", "nngp"),
          ]:
              ntkgp_get = get + ("ntkgp",)
              if "ntk" not in get:
                  get += ("ntk",)
              k_dd = kernel_fn(x_train, None, get)
  
              always_ntk = self._always_ntk(kernel_fn)
              always_ntk_k_dd = always_ntk(x_train, None, get)
  
              gp_inference = predict.gp_inference(
                  k_dd, y_train, diag_reg=reg
              )
  
              always_ntk_gp_inference = predict.gp_inference(
                  always_ntk_k_dd, y_train, diag_reg=reg
              )
              gd_ensemble = predict.gradient_descent_mse_ensemble(
                  kernel_fn, x_train, y_train, diag_reg=reg
              )
              for x_test in [None, "x_test"]:
                  x_test = (
                      None
                      if x_test is None
                      else random.normal(key, (8, 2))
                  )
                  k_td = (
                      None
                      if x_test is None
                      else kernel_fn(x_test, x_train, get)
                  )
                  always_ntk_k_td = (
                      None
                      if x_test is None
                      else always_ntk(x_test, x_train)
                  )
  
                  for compute_cov in [True, False]:
                      with self.subTest(
                          kernel_fn_is_analytic=kernel_fn_is_analytic,
                          get=ntkgp_get,
                          x_test=x_test if x_test is None else "x_test",
                          compute_cov=compute_cov,
                      ):
                          if compute_cov:
                              k_tt = (
                                  True
                                  if x_test is None
                                  else kernel_fn(x_test, None, get)
                              )
                              always_ntk_tt = (
                                  True
                                  if x_test is None
                                  else kernel_fn(x_test, None, "ntk")
                              )
  
                          else:
                              k_tt = None
                              always_ntk_tt = None
  
                          if (
                              "nngp" not in get
                              and "ntk" in ntkgp_get
                              and compute_cov
                              and k_td is not None
                          ):
                              with self.assertRaises(ValueError):
                                  out_gp_inf = gp_inference(
                                      get=ntkgp_get,
                                      k_test_train=k_td,
                                      k_test_test=k_tt,
                                  )
                          else:
                              out_gp_inf = gp_inference(
                                  get=ntkgp_get,
                                  k_test_train=k_td,
                                  k_test_test=k_tt,
                              )
                              out_ens = gd_ensemble(
                                  None, x_test, get, compute_cov
                              )
                              out_always_ntk_gp_inf = (
                                  always_ntk_gp_inference(
                                      get="nngp",
                                      k_test_train=always_ntk_k_td,
                                      k_test_test=always_ntk_tt,
                                  )
                              )
  
                              # Compare ntkgp predictions to nngp code, with hacked kernel
                              for g in ntkgp_get:
                                  self.assertAllClose(
                                      getattr(out_gp_inf, g),
                                      (
                                          getattr(out_ens, g)
                                          if g != "ntkgp"
                                          else out_always_ntk_gp_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 16 for calling the PredictTest obj's underlying member method code with example usage: obj.testGpInference() and returns: kernel_fn_empirical