Factorizable Joint Shift in Multinomial Classification
This work addresses dataset shift issues in machine learning classification, but it is incremental as it builds on prior concepts without introducing a new paradigm.
The paper tackles the problem of factorizable joint shift in multinomial classification by deriving a representation for it and proposing alternative estimation methods, while showing that it is not fully identifiable without test class labels.
Factorizable joint shift (FJS) was recently proposed as a type of dataset shift for which the complete characteristics can be estimated from feature data observations on the test dataset by a method called Joint Importance Aligning. For the multinomial (multiclass) classification setting, we derive a representation of factorizable joint shift in terms of the source (training) distribution, the target (test) prior class probabilities and the target marginal distribution of the features. On the basis of this result, we propose alternatives to joint importance aligning and, at the same time, point out that factorizable joint shift is not fully identifiable if no class label information on the test dataset is available and no additional assumptions are made. Other results of the paper include correction formulae for the posterior class probabilities both under general dataset shift and factorizable joint shift. In addition, we investigate the consequences of assuming factorizable joint shift for the bias caused by sample selection.