code: def test_kissgp_gp_mean_abs_error(self):
      train_x, train_y, test_x, test_y = make_data()
      train_dataset = TensorDataset(train_x, train_y)
      train_loader = DataLoader(
          train_dataset, shuffle=True, batch_size=64
      )
  
      model = GPRegressionModel()
      likelihood = GaussianLikelihood()
      mll = gpytorch.mlls.VariationalELBO(
          likelihood, model, num_data=len(train_y)
      )
      # We use SGD here, rather than Adam
      # Emperically, we find that SGD is better for variational regression
      optimizer = torch.optim.Adam(
          [
              {"params": model.parameters()},
              {"params": likelihood.parameters()},
          ],
          lr=0.01,
      )
  
      # Our loss object
      # We're using the VariationalELBO object
      mll = gpytorch.mlls.VariationalELBO(
          likelihood, model, num_data=train_y.size(0)
      )
  
      # The training loop
      def train(n_epochs=15):
          # We use a Learning rate scheduler from PyTorch to lower the learning rate during optimization
          # We're going to drop the learning rate by 1/10 after 3/4 of training
          # This helps the model converge to a minimum
          scheduler = torch.optim.lr_scheduler.MultiStepLR(
              optimizer, milestones=[0.75 * n_epochs], gamma=0.1
          )
  
          for _ in range(n_epochs):
              for x_batch, y_batch in train_loader:
                  x_batch = x_batch.float()
                  y_batch = y_batch.float()
                  optimizer.zero_grad()
                  output = model(x_batch)
                  loss = -mll(output, y_batch)
                  loss.backward()
                  optimizer.step()
  
              scheduler.step()
  
      train()
  
      for _, param in model.named_parameters():
          self.assertTrue(param.grad is not None)
          self.assertGreater(param.grad.norm().item(), 0)
      for param in likelihood.parameters():
          self.assertTrue(param.grad is not None)
          self.assertGreater(param.grad.norm().item(), 0)
  
          # Test the model
          model.eval()
          likelihood.eval()
  
          test_preds = likelihood(model(test_x)).mean
          mean_abs_error = torch.mean(torch.abs(test_y - test_preds))
  
      self.assertLess(mean_abs_error.squeeze().item(), 0.1)
  
imports: import os
  import random
  import unittest
  from math import exp, pi
  import torch
  from torch.utils.data import DataLoader, TensorDataset
  import gpytorch
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.kernels import RBFKernel, ScaleKernel
  from gpytorch.likelihoods import GaussianLikelihood
  from gpytorch.means import ConstantMean
  from gpytorch.priors import SmoothedBoxPrior
label_desc: Use image node_id 3 for calling the TestKISSGPVariationalRegression obj's underlying member method code with example usage: obj.test_kissgp_gp_mean_abs_error() without return types