code: def test_train_and_eval(self):
      likelihood = MultitaskGaussianLikelihood(num_tasks=4)
      model = LMCModel()
  
      # Find optimal model hyperparameters
      model.train()
      likelihood.train()
      optimizer = torch.optim.Adam(
          [
              {"params": model.parameters()},
              {"params": likelihood.parameters()},
          ],
          lr=0.01,
      )
  
      # Our loss object. We're using the VariationalELBO, which essentially just computes the ELBO
      mll = gpytorch.mlls.VariationalELBO(
          likelihood, model, num_data=train_y.size(0)
      )
  
      # We use more CG iterations here because the preconditioner introduced in the NeurIPS paper seems to be less
      # effective for VI.
      for i in range(400):
          # Within each iteration, we will go over each minibatch of data
          optimizer.zero_grad()
          output = model(train_x)
          loss = -mll(output, train_y)
          loss.backward()
          optimizer.step()
  
          for param in model.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()
  
      # Make predictions for both sets of test points, and check MAEs.
      with torch.no_grad(), gpytorch.settings.max_eager_kernel_size(1):
          batch_predictions = likelihood(model(train_x))
          preds1 = batch_predictions.mean[:, 0]
          preds2 = batch_predictions.mean[:, 1]
          preds3 = batch_predictions.mean[:, 2]
          preds4 = batch_predictions.mean[:, 3]
          mean_abs_error1 = torch.mean(
              torch.abs(train_y[..., 0] - preds1)
          )
          mean_abs_error2 = torch.mean(
              torch.abs(train_y[..., 1] - preds2)
          )
          mean_abs_error3 = torch.mean(
              torch.abs(train_y[..., 2] - preds3)
          )
          mean_abs_error4 = torch.mean(
              torch.abs(train_y[..., 3] - preds4)
          )
          self.assertLess(mean_abs_error1.squeeze().item(), 0.15)
          self.assertLess(mean_abs_error2.squeeze().item(), 0.15)
          self.assertLess(mean_abs_error3.squeeze().item(), 0.15)
          self.assertLess(mean_abs_error4.squeeze().item(), 0.15)
  
          # Smoke test for getting predictive uncertainties
          lower, upper = batch_predictions.confidence_region()
          self.assertEqual(lower.shape, train_y.shape)
          self.assertEqual(upper.shape, train_y.shape)
  
file_path: gpytorch/test/examples/test_lmc_svgp_regression.py
imports: import math
  import os
  import random
  import unittest
  import torch
  import gpytorch
  from gpytorch.likelihoods import GaussianLikelihood, MultitaskGaussianLikelihood
label_desc: Use image node_id 3 for calling the TestIndependentMultitaskGPRegression obj's underlying member method code with example usage: obj.test_train_and_eval() without return types