code: def maximum_likelihood_estimate_sgd(
      distr_output: DistributionOutput,
      samples: mx.ndarray,
      init_biases: List[mx.ndarray.NDArray] = None,
      num_epochs: PositiveInt = PositiveInt(5),
      learning_rate: PositiveFloat = PositiveFloat(1e-2),
      hybridize: bool = True,
  ) -> List[np.ndarray]:
      model_ctx = mx.cpu()
  
      arg_proj = distr_output.get_args_proj()
      arg_proj.initialize()
  
      if hybridize:
          arg_proj.hybridize()
  
      if init_biases is not None:
          for param, bias in zip(arg_proj.proj, init_biases):
              param.params[param.prefix + "bias"].initialize(
                  mx.initializer.Constant(bias), force_reinit=True
              )
  
      trainer = mx.gluon.Trainer(
          arg_proj.collect_params(),
          "sgd",
          {"learning_rate": learning_rate, "clip_gradient": 10.0},
      )
  
      # The input data to our model is one-dimensional
      dummy_data = mx.nd.array(np.ones((len(samples), 1)))
  
      train_data = mx.gluon.data.DataLoader(
          mx.gluon.data.ArrayDataset(dummy_data, samples),
          batch_size=BATCH_SIZE,
          shuffle=True,
      )
  
      for e in range(num_epochs):
          cumulative_loss = 0
          num_batches = 0
          # inner loop
          for i, (data, sample_label) in enumerate(train_data):
              data = data.as_in_context(model_ctx)
              sample_label = sample_label.as_in_context(model_ctx)
              with mx.autograd.record():
                  distr_args = arg_proj(data)
                  distr = distr_output.distribution(distr_args)
                  loss = distr.loss(sample_label)
                  if not hybridize:
                      assert loss.shape == distr.batch_shape
              loss.backward()
  
              trainer.step(BATCH_SIZE)
              num_batches += 1
  
              cumulative_loss += mx.nd.mean(loss).asscalar()
  
              assert not np.isnan(cumulative_loss)
          print(
              "Epoch {}, loss: {}".format(
                  e, cumulative_loss / num_batches
              )
          )
  
      if len(distr_args[0].shape) == 1:
          return [
              param.asnumpy()
              for param in arg_proj(mx.nd.array(np.ones((1, 1))))
          ]
  
      # alpha parameter of zero inflated Neg Bin was not returned using param[0]
      ls = [
          [p.asnumpy() for p in param]
          for param in arg_proj(mx.nd.array(np.ones((1, 1))))
      ]
      return reduce(lambda x, y: x + y, ls)
  
imports: from functools import reduce
  from typing import List, Tuple
  import mxnet
  import numpy
  import pytest
  from gluonts.mx.model.tpp.distribution import Loglogistic, LoglogisticOutput, Weibull, WeibullOutput
  from gluonts.mx.distribution import Beta, BetaOutput, Binned, BinnedOutput, Categorical, CategoricalOutput, Dirichlet, DirichletMultinomial, DirichletMultinomialOutput, DirichletOutput, DistributionOutput, EmpiricalDistributionOutput, Gamma, GammaOutput, Gaussian, GaussianOutput, GenPareto, GenParetoOutput, Laplace, LaplaceOutput, LogitNormal, LogitNormalOutput, LowrankMultivariateGaussian, LowrankMultivariateGaussianOutput, MultivariateGaussian, MultivariateGaussianOutput, NegativeBinomial, NegativeBinomialOutput, OneInflatedBeta, OneInflatedBetaOutput, PiecewiseLinear, PiecewiseLinearOutput, Poisson, PoissonOutput, StudentT, StudentTOutput, ZeroAndOneInflatedBeta, ZeroAndOneInflatedBetaOutput, ZeroInflatedBeta, ZeroInflatedBetaOutput, ZeroInflatedNegativeBinomialOutput, ZeroInflatedPoissonOutput
  from gluonts.mx.distribution.box_cox_transform import InverseBoxCoxTransform, InverseBoxCoxTransformOutput
  from gluonts.mx.distribution.transformed_distribution import TransformedDistribution
  from gluonts.mx.distribution.transformed_distribution_output import TransformedDistributionOutput
  from gluonts.pydantic import PositiveFloat, PositiveInt
label_desc: Use image node_id 2 for calling a global function with example usage: maximum_likelihood_estimate_sgd(distr_output, samples, init_biases, num_epochs, learning_rate, hybridize) and returns: reduce, unknown