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# Source code for tllib.ranking.nce

"""
@author: Yong Liu
@contact: liuyong1095556447@163.com
"""
import numpy as np

__all__ = ['negative_conditional_entropy']

[docs]def negative_conditional_entropy(source_labels: np.ndarray, target_labels: np.ndarray):
r"""
Negative Conditional Entropy in Transferability and Hardness of Supervised
Classification Tasks (ICCV 2019) <https://arxiv.org/pdf/1908.08142v1.pdf>_.

The NCE :math:\mathcal{H} can be described as:

.. math::
\mathcal{H}=-\sum_{y \in \mathcal{C}_t} \sum_{z \in \mathcal{C}_s} \hat{P}(y, z) \log \frac{\hat{P}(y, z)}{\hat{P}(z)}

where :math:\hat{P}(z) is the empirical distribution and :math:\hat{P}\left(y \mid z\right) is the empirical
conditional distribution estimated by source and target label.

Args:
source_labels (np.ndarray): predicted source labels.
target_labels (np.ndarray): groud-truth target labels.

Shape:
- source_labels: (N, ) elements in [0, :math:C_s), with source class number :math:C_s.
- target_labels: (N, ) elements in [0, :math:C_t), with target class number :math:C_t.
"""
C_t = int(np.max(target_labels) + 1)
C_s = int(np.max(source_labels) + 1)
N = len(source_labels)

joint = np.zeros((C_t, C_s), dtype=float)  # placeholder for the joint distribution, shape [C_t, C_s]
for s, t in zip(source_labels, target_labels):
s = int(s)
t = int(t)
joint[t, s] += 1.0 / N
p_z = joint.sum(axis=0, keepdims=True)

p_target_given_source = (joint / p_z).T  # P(y | z), shape [C_s, C_t]
mask = p_z.reshape(-1) != 0  # valid Z, shape [C_s]
p_target_given_source = p_target_given_source[mask] + 1e-20  # remove NaN where p(z) = 0, add 1e-20 to avoid log (0)
entropy_y_given_z = np.sum(- p_target_given_source * np.log(p_target_given_source), axis=1, keepdims=True)
conditional_entropy = np.sum(entropy_y_given_z * p_z.reshape((-1, 1))[mask])

return -conditional_entropy


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