class_docstr: The Laplace distribution with location `loc` and `scale` parameters.
  
  #### Mathematical details
  
  The probability density function (pdf) of this distribution is,
  
  ```none
  pdf(x; mu, sigma) = exp(-|x - mu| / sigma) / Z
  Z = 2 sigma
  ```
  
  where `loc = mu`, `scale = sigma`, and `Z` is the normalization constant.
  
  Note that the Laplace distribution can be thought of two exponential
  distributions spliced together 'back-to-back.'
  
  The Laplace distribution is a member of the [location-scale family](
  https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
  constructed as,
  
  ```none
  X ~ Laplace(loc=0, scale=1)
  Y = loc + scale * X
  ```
code: def _maximum_likelihood_parameters(cls, value):
      median = quantiles.percentile(
          value, 50.0, axis=0, interpolation="linear"
      )
      return {
          "loc": median,
          "scale": tf.reduce_mean(tf.abs(value - median), axis=0),
      }
  
imports: import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import identity
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import distribution
  from tensorflow_probability.python.distributions import kullback_leibler
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import reparameterization
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import special_math
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow_probability.python.stats import quantiles
label_desc: Use image node_id 20 for calling the Laplace obj's underlying member method code with example usage: obj._maximum_likelihood_parameters(cls, value) and returns: dict