Quantification is a supervised machine learning task, focused on estimating
the class prevalence of a dataset rather than labeling its individual
observations. We introduce Continuous Sweep, a new parametric binary quantifier
inspired by the well-performing Median Sweep. Median Sweep is currently one of
the best binary quantifiers, but we have changed this quantifier on three
points, namely 1) using parametric class distributions instead of empirical
distributions, 2) optimizing decision boundaries instead of applying discrete
decision rules, and 3) calculating the mean instead of the median. We derive
analytic expressions for the bias and variance of Continuous Sweep under
general model assumptions. This is one of the first theoretical contributions
in the field of quantification learning. Moreover, these derivations enable us
to find the optimal decision boundaries. Finally, our simulation study shows
that Continuous Sweep outperforms Median Sweep in a wide range of situations.

通过引入连续扫描（Continuous Sweep）这种新的参数二值量化器来估计数据集的类别普遍性，其使用了参数类分布替代经验分布，优化了决策边界和采用了平均值，同时通过理论推导得到了偏差和方差的解析表达式。模拟研究结果表明，连续扫描在广泛的情况下优于中位数扫描（Median Sweep） 。