text: import torch
  import gpytorch
  from gpytorch.models import ApproximateGP
  from gpytorch.variational import CholeskyVariationalDistribution
  from gpytorch.variational import IndependentMultitaskVariationalStrategy
  from utils.logger import setup_custom_logger
  import os
  
  
  log = setup_custom_logger(os.path.basename(__file__))
  
  
  class InducingGPClassificationModel(ApproximateGP):
      def __init__(self,
                   inducing_points,
                   num_classes,
                   ard_num_dims=None,
                   initial_lengthscale=None,
                   initial_outputscale=None,
                   learn_inducing_locations=True,
                   lengthscale_prior_alpha=None,
                   lengthscale_prior_beta=None):
          """
          Initializes a variational Gaussian process classifier with the given inducing points and whitening.
  
          :param inducing_points: Tensor containing the inducing point locations, shape [num_inducing_points, num_features]
          :param num_classes: number of classes
          :param ard_num_dims: number of feature dimensions for ARD prior, or None for shared lengthscale
          :param initial_lengthscale: initial value for all length scales
          :param initial_outputscale: initial value for all output scales
          :param learn_inducing_locations: whether or not to adjust the inducing locations
          :param lengthscale_prior_alpha: concentration parameter alpha of Gamma distribution used as lengthscale prior
          :param lengthscale_prior_beta: rate parameter beta of Gamma distribution used as lengthscale prior
          """
  
          # Ensure both alpha and beta, or none of them are set
          assert (lengthscale_prior_alpha is not None) == (lengthscale_prior_beta is not None), "Either both alpha and beta or none of them must be set"
  
          # Set up variational distribution with full covariance
          num_inducing_points = len(inducing_points)
          variational_distribution = CholeskyVariationalDistribution(num_inducing_points=num_inducing_points, batch_shape=torch.Size([num_classes]))
  
          base_variational_strategy = gpytorch.variational.VariationalStrategy(
              model=self,
              inducing_points=inducing_points,
              variational_distribution=variational_distribution,
              learn_inducing_locations=learn_inducing_locations
          )
  
          # Produce a `MultitaskMultivariateNormal` distribution with one task per class
          variational_strategy = IndependentMultitaskVariationalStrategy(base_variational_strategy, num_tasks=num_classes)
  
          super(InducingGPClassificationModel, self).__init__(variational_strategy)
          self.mean_module = gpytorch.means.ZeroMean()
  
          # Lengthscale prior
          lengthscale_prior = None
          if lengthscale_prior_alpha is not None:
              log.info(f"Setting lengthscale prior with alpha = {lengthscale_prior_alpha} and beta = {lengthscale_prior_beta}")
              lengthscale_prior = gpytorch.priors.GammaPrior(lengthscale_prior_alpha, lengthscale_prior_beta)
  
          # Covariance kernel: ScaleKernel + RBFKernel
          rbf_kernel = gpytorch.kernels.RBFKernel(batch_shape=torch.Size([num_classes]), ard_num_dims=ard_num_dims, lengthscale_prior=lengthscale_prior)
          scale_kernel = gpytorch.kernels.ScaleKernel(rbf_kernel, batch_shape=torch.Size([num_classes]))
  
          # Set initial length scale
          if initial_lengthscale is not None:
              log.info(f"Initializing lengthscale to {initial_lengthscale}")
              rbf_kernel.lengthscale = initial_lengthscale
  
          # Set initial scale
          if initial_outputscale is not None:
              log.info(f"Initializing outputscale to {initial_outputscale}")
              scale_kernel.outputscale = initial_outputscale
  
          self.covar_module = scale_kernel
  
      def forward(self, x):
          mean_x = self.mean_module(x)
          covar_x = self.covar_module(x)
          latent_pred = gpytorch.distributions.MultivariateNormal(mean_x, covar_x)
          return latent_pred
  