class_docstr: Class for the Fisher information metric on multinomial distributions.
  
  The Fisher information metric on the $n$-simplex of multinomial
  distributions parameters can be obtained as the pullback metric of the
  $n$-sphere using the componentwise square root.
  
  References
  ----------
  .. [K2003] R. E. Kass. The Geometry of Asymptotic Inference. Statistical
      Science, 4(3): 188 - 234, 1989.
docstr: Compute the exponential map.
  
  Compute the exponential map associated to the Fisher information
  metric by pulling back the exponential map on the sphere by the
  simplex_to_sphere map.
  
  Parameters
  ----------
  tangent_vec : array-like, shape=[..., dim + 1]
      Tangent vector at base point.
  base_point : array-like, shape=[..., dim + 1]
      Base point.
  
  Returns
  -------
  exp : array-like, shape=[..., dim + 1]
      End point of the geodesic starting at base_point with
      initial velocity tangent_vec and stopping at time 1.
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code: def exp(self, tangent_vec, base_point):
      """Compute the exponential map.
  
      Compute the exponential map associated to the Fisher information
      metric by pulling back the exponential map on the sphere by the
      simplex_to_sphere map.
  
      Parameters
      ----------
      tangent_vec : array-like, shape=[..., dim + 1]
          Tangent vector at base point.
      base_point : array-like, shape=[..., dim + 1]
          Base point.
  
      Returns
      -------
      exp : array-like, shape=[..., dim + 1]
          End point of the geodesic starting at base_point with
          initial velocity tangent_vec and stopping at time 1.
      """
      base_point_sphere = self.simplex_to_sphere(base_point)
      tangent_vec_sphere = self.tangent_simplex_to_sphere(
          tangent_vec, base_point
      )
      exp_sphere = self._sphere.metric.exp(
          tangent_vec_sphere, base_point_sphere
      )
  
      return self.sphere_to_simplex(exp_sphere)
  
imports: from scipy.stats import dirichlet, multinomial
  import geomstats.backend
  from geomstats.algebra_utils import from_vector_to_diagonal_matrix
  from geomstats.geometry.base import LevelSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.hypersphere import Hypersphere
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.information_geometry.base import InformationManifoldMixin, ScipyMultivariateRandomVariable
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 7 for calling the MultinomialMetric obj's underlying member method code with example usage: obj.exp(tangent_vec, base_point) and returns: self