def _auc_convert_hist_to_auc(hist_true_acc, hist_false_acc, nbins):
"""Convert histograms to auc.
Args:
hist_true_acc: `Tensor` holding accumulated histogram of scores for records
that were `True`.
hist_false_acc: `Tensor` holding accumulated histogram of scores for
records that were `False`.
nbins: Integer number of bins in the histograms.
Returns:
Scalar `Tensor` estimating AUC.
"""
# Note that this follows the "Approximating AUC" section in:
# Efficient AUC learning curve calculation, R. R. Bouckaert,
# AI'06 Proceedings of the 19th Australian joint conference on Artificial
# Intelligence: advances in Artificial Intelligence
# Pages 181-191.
# Note that the above paper has an error, and we need to re-order our bins to
# go from high to low score.
# Normalize histogram so we get fraction in each bin.
normed_hist_true = math_ops.truediv(hist_true_acc,
math_ops.reduce_sum(hist_true_acc))
normed_hist_false = math_ops.truediv(hist_false_acc,
math_ops.reduce_sum(hist_false_acc))
# These become delta x, delta y from the paper.
delta_y_t = array_ops.reverse(normed_hist_true, [True], name='delta_y_t')
delta_x_t = array_ops.reverse(normed_hist_false, [True], name='delta_x_t')
# strict_1d_cumsum requires float32 args.
delta_y_t = math_ops.cast(delta_y_t, dtypes.float32)
delta_x_t = math_ops.cast(delta_x_t, dtypes.float32)
# Trapezoidal integration, \int_0^1 0.5 * (y_t + y_{t-1}) dx_t
y_t = _strict_1d_cumsum(delta_y_t, nbins)
first_trap = delta_x_t[0] * y_t[0] / 2.0
other_traps = delta_x_t[1:] * (y_t[1:] + y_t[:nbins - 1]) / 2.0
return math_ops.add(first_trap, math_ops.reduce_sum(other_traps), name='auc')
# TODO(langmore) Remove once a faster cumsum (accumulate_sum) Op is available.
# Also see if cast to float32 above can be removed with new cumsum.
# See: https://github.com/tensorflow/tensorflow/issues/813
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