Source code for geomstats.information_geometry.categorical

"""Statistical Manifold of categorical distributions with the Fisher metric.

Lead author: Alice Le Brigant.

from geomstats.information_geometry.multinomial import (

[docs] class CategoricalDistributions(MultinomialDistributions): r"""Class for the manifold of categorical distributions. This is the set of `n+1`-tuples of positive reals that sum up to one, i.e. the `n`-simplex. Each point is the parameter of a categorical distribution, i.e. gives the probabilities of $n$ different outcomes in a single experiment. Attributes ---------- dim : int Dimension of the manifold of categorical distributions. The number of outcomes is dim + 1. embedding_manifold : Manifold Embedding manifold. """ def __init__(self, dim, equip=True): super().__init__(dim=dim, n_draws=1, equip=equip)
[docs] @staticmethod def default_metric(): """Metric to equip the space with if equip is True.""" return CategoricalMetric
[docs] class CategoricalMetric(MultinomialMetric): """Class for the Fisher information metric on categorical distributions. The Fisher information metric on the $n$-simplex of categorical 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. """