code: def test_deterministic_l1(mu: float, hybridize: bool) -> None:
      """
      Test to check that maximizing the likelihood recovers the parameters.
      This tests uses the Laplace distribution with fixed variance and sample mean.
      This essentially reduces to determistic L1.
      """
      # generate samples
      mu = mu
      mus = mx.nd.zeros(NUM_SAMPLES) + mu
  
      class LaplaceFixedVarianceOutput(LaplaceOutput):
          @classmethod
          def domain_map(cls, F, mu, b):
              b = 0.1 * F.ones_like(b)
              return mu.squeeze(axis=-1), b.squeeze(axis=-1)
  
      deterministic_distr = Laplace(
          mu=mus, b=0.1 * mx.nd.ones_like(mus)
      )
      samples = deterministic_distr.sample()
  
      mu_hat, _ = maximum_likelihood_estimate_sgd(
          LaplaceFixedVarianceOutput(),
          samples,
          init_biases=[3 * mu, 0.1],
          learning_rate=PositiveFloat(1e-3),
          hybridize=hybridize,
      )
  
      assert (
          np.abs(mu_hat - mu) < TOL * mu
      ), f"mu did not match: mu = {mu}, mu_hat = {mu_hat}"
  
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 14 for calling a global function with example usage: test_deterministic_l1(mu, hybridize) and returns: mu,  b