Active learning (AL) is a semi-supervised learning paradigm with human-machine interaction and a limited annotation budget. However, few AL studies have explored distribution inconsistency between the data and the population. In this paper, we consider a basic form of the aforementioned issue,i.e., the training data is non-independently and identically distributed (non-IID) sampled from a class uniformly distributed population. Accordingly, we propose a naïve sample selection plugin, namely generalized active stratified sampling (GASS), to rebalance the sample size of each class during AL iterative process, resulting in a progressive approximation to the population. We generalize statistical stratified sampling to support the uncertainty strata criterion, forming the statistical foundation of GASS. This method, as a plugin, can seamlessly collaborate with popular information-based strategies. GASS shows superior rebalancing capabilities by analyzing the statistical moment and the class imbalanced index under the Probably Approximately Correct (PAC) theory. Furthermore, models derived with GASS have low Rademacher complexity (RC), indicating low generalization error bounds, and GASS also exhibits strong robustness to prediction perturbations. Experiments were conducted on 5 benchmark image datasets, and the results show that GASS significantly boosts the test accuracy by about$2.38\%$/$3.19\%$(paired$t$-test$p=0.01$/0.04) and reduces the empirical RC by about$1.42\%$/$1.94\%$(paired$t$-test$p=0.01$/0.05) on average in class imbalanced/balanced scenarios, respectively. This study establishes a potential benchmark for information-based AL.

Sample selection is to select a number of representative samples from a large database such that a learning algorithm can have a reduced computational cost and an improved learning accuracy. This paper gives a new sample selection mechanism, i.e., the maximum ambiguity-based sample selection in fuzzy decision tree induction. Compared with the existing sample selection methods, this mechanism selects the samples based on the principle of maximal classification ambiguity. The major advantage of this mechanism is that the adjustment of the fuzzy decision tree is minimized when adding selected samples to the training set. This advantage is confirmed via the theoretical analysis of the leaf-nodes' frequency in the decision trees. The decision tree generated from the selected samples usually has a better performance than that from the original database. Furthermore, experimental results show that generalization ability of the tree based on our selection mechanism is far more superior to that based on random selection mechanism.

The fuzzy-rough set (FRS) methodology, as a useful tool to handle discernibility and fuzziness, has been widely studied. Some researchers studied on the rough approximation of fuzzy sets, while some others focused on studying one application of FRS: attribute reduction (i.e., feature selection). However, constructing classifier by using FRS, as another application of FRS, has been less studied. In this paper, we build a rule-based classifier by using one generalized FRS model after proposing a new concept named as ¿consistence degree¿ which is used as the critical value to keep the discernibility information invariant in the processing of rule induction. First, we generalized the existing FRS to a robust model with respect to misclassification and perturbation by incorporating one controlled threshold into knowledge representation of FRS. Second, we propose a concept named as ¿consistence degree¿ and by the strict mathematical reasoning, we show that this concept is reasonable as a critical value to reduce redundant attribute values in database. By employing this concept, we then design a discernibility vector to develop the algorithms of rule induction. The induced rule set can function as a classifier. Finally, the experimental results show that the proposed rule-based classifier is feasible and effective on noisy data.