code: def test_multitask_low_rank_noise_covar(self):
      likelihood = MultitaskGaussianLikelihood(num_tasks=2, rank=1)
      model = MultitaskGPModel(train_x, train_y, likelihood)
      # Find optimal model hyperparameters
      model.train()
      likelihood.train()
  
      # Use the adam optimizer
      optimizer = torch.optim.Adam(
          model.parameters(), lr=0.1
      )  # Includes GaussianLikelihood parameters
  
      # "Loss" for GPs - the marginal log likelihood
      mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)
  
      n_iter = 50
      for _ in range(n_iter):
          # Zero prev backpropped gradients
          optimizer.zero_grad()
          # Make predictions from training data
          # Again, note feeding duplicated x_data and indices indicating which task
          output = model(train_x)
          # TODO: Fix this view call!!
          loss = -mll(output, train_y)
          loss.backward()
          optimizer.step()
  
      # Test the model
      model.eval()
      likelihood.eval()
  
      num_tasks = 2
      task_noise_covar_factor = likelihood.task_noise_covar_factor
      noise = likelihood.noise
      task_noise_covar = task_noise_covar_factor.matmul(
          task_noise_covar_factor.transpose(-1, -2)
      ) + noise * torch.eye(num_tasks)
  
      self.assertGreater(task_noise_covar[0, 1].item(), 0.05)
  
file_path: gpytorch/test/likelihoods/test_general_multitask_gaussian_likelihood.py
imports: import os
  import random
  import unittest
  from math import pi
  import torch
  import gpytorch
  from gpytorch.distributions import MultitaskMultivariateNormal
  from gpytorch.kernels import MultitaskKernel, RBFKernel
  from gpytorch.likelihoods import MultitaskGaussianLikelihood
  from gpytorch.means import ConstantMean, MultitaskMean
label_desc: Use image node_id 3 for calling the TestMultiTaskGPRegression obj's underlying member method code with example usage: obj.test_multitask_low_rank_noise_covar() without return types