We study the problem of class distribution estimation under dataset shift. On
the training dataset, both features and class labels are observed while on the
test dataset only the features can be observed. The task then is the estimation
of the distribution of the class labels, i.e. the estimation of the class prior
probabilities, in the test dataset. Assumptions of invariance between the
training joint distribution of features and labels and the test distribution
can considerably facilitate this task. We discuss the assumptions of covariate
shift, factorizable joint shift, and sparse joint shift and their implications
for class distribution estimation.

我们研究了在数据集偏移下的类别分布估计问题，讨论了协变量转移、可因子化联合转移和稀疏联合转移的假设及其对类别分布估计的影响。

类分布估计的不变性假设

Invariance assumptions for class distribution estimation

We introduce Fisher consistency in the sense of unbiasedness as a desirable
property for estimators of class prior probabilities. Lack of Fisher
consistency could be used as a criterion to dismiss estimators that are
unlikely to deliver precise estimates in test datasets under prior probability
and more general dataset shift. The usefulness of this unbiasedness concept is
demonstrated with three examples of classifiers used for quantification:
Adjusted Classify & Count, EM-algorithm and CDE-Iterate. We find that Adjusted
Classify & Count and EM-algorithm are Fisher consistent. A counter-example
shows that CDE-Iterate is not Fisher consistent and, therefore, cannot be
trusted to deliver reliable estimates of class probabilities.

介绍了 Fisher 一致性作为无偏性估计量的可取属性，通过三个分类器的实例证明无偏性概念的实用性。