dataeval.metrics.estimators.ber
===============================

.. py:function:: dataeval.metrics.estimators.ber(images, labels, k = 1, method = 'KNN')

   An estimator for Multi-class :term:`Bayes error rate<Bayes Error Rate (BER)>` using FR or KNN test statistic basis

   :param images: Array of images or image :term:`embeddings<Embeddings>`
   :type images: ArrayLike (N, ... )
   :param labels: Array of labels for each image or image embedding
   :type labels: ArrayLike (N, 1)
   :param k: Number of nearest neighbors for KNN estimator -- ignored by MST estimator
   :type k: int, default 1
   :param method: Method to use when estimating the Bayes error rate
   :type method: Literal["KNN", "MST"], default "KNN"

   :returns: The upper and lower bounds of the Bayes Error Rate
   :rtype: BEROutput

   .. rubric:: References

   [1] `Learning to Bound the Multi-class Bayes Error (Th. 3 and Th. 4) <https://arxiv.org/abs/1811.06419>`_

   .. rubric:: Examples

   >>> import sklearn.datasets as dsets
   >>> from dataeval.metrics.estimators import ber

   >>> images, labels = dsets.make_blobs(n_samples=50, centers=2, n_features=2, random_state=0)

   >>> ber(images, labels)
   BEROutput(ber=0.04, ber_lower=0.020416847668728033)