code: def test_train_and_eval(self):
      # We're manually going to set the hyperparameters to something they shouldn't be
      likelihood = MultitaskGaussianLikelihood(num_tasks=2)
      gp_model = ExactGPModel(train_x, train_y12, likelihood)
      mll = gpytorch.ExactMarginalLogLikelihood(likelihood, gp_model)
  
      # Find optimal model hyperparameters
      gp_model.train()
      likelihood.train()
      optimizer = optim.Adam(gp_model.parameters(), lr=0.1)
      optimizer.n_iter = 0
      for _ in range(75):
          optimizer.zero_grad()
          output = gp_model(train_x)
          loss = -mll(output, train_y12).sum()
          loss.backward()
          optimizer.step()
  
          for param in gp_model.parameters():
              self.assertTrue(param.grad is not None)
              self.assertGreater(param.grad.norm().item(), 0)
  
      # Test the model
      gp_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(gp_model(test_x))
          preds1 = batch_predictions.mean[:, 0]
          preds2 = batch_predictions.mean[:, 1]
          mean_abs_error1 = torch.mean(torch.abs(test_y1 - preds1))
          mean_abs_error2 = torch.mean(torch.abs(test_y2 - preds2))
          self.assertLess(mean_abs_error1.squeeze().item(), 0.01)
          self.assertLess(mean_abs_error2.squeeze().item(), 0.01)
  
          # Smoke test for getting predictive uncertainties
          lower, upper = batch_predictions.confidence_region()
          self.assertEqual(lower.shape, test_y12.shape)
          self.assertEqual(upper.shape, test_y12.shape)
  
file_path: gpytorch/test/examples/test_independent_multitask_gp_regression.py
imports: import math
  import os
  import random
  import unittest
  import torch
  from torch import optim
  import gpytorch
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from gpytorch.kernels import RBFKernel, ScaleKernel
  from gpytorch.likelihoods import MultitaskGaussianLikelihood
  from gpytorch.means import ConstantMean
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