Partial label learning (PLL) is to learn a discriminative model under incomplete supervision, where each instance is annotated with a candidate label set. The basic principle of PLL is that the unknown correct label y of an instance x resides in its candidate label set s, i.e., P(y ∈ s | x) = 1. On which basis, current researches either directly model P(x | y) under different data generation assumptions or propose various surrogate multiclass losses, which all aim to encourage the model-based Pθ(y ∈ s | x)→1 implicitly. In this work, instead, we explicitly construct a binary classification task toward P(y ∈ s | x) based on the discriminative model, that is to predict whether the model-output label of x is one of its candidate labels. We formulate a novel risk estimator with estimation error bound for the proposed PLL binary classification risk. By applying logit adjustment based on disambiguation strategy, the practical approach directly maximizes Pθ(y ∈ s | x) while implicitly disambiguating the correct one from candidate labels simultaneously. Thorough experiments validate that the proposed approach achieves competitive performance against the state-of-the-art PLL methods.

Rule-based classifier, that extract a subset of induced rules to efficiently learn/mine while preserving the discernibility information, plays a crucial role in human-explainable artificial intelligence. However, in this era of big data, rule induction on the whole datasets is computationally intensive. So far, to the best of our knowledge, no known method focusing on accelerating rule induction has been reported. This is the first study to consider the acceleration technique to reduce the scale of computation in rule induction. We propose an accelerator for rule induction based on fuzzy rough theory; the accelerator can avoid redundant computation and accelerate the building of a rule classifier. First, a rule induction method based on consistence degree, called consistence-based value reduction (CVR), is proposed and used as basis to accelerate. Second, we introduce a compacted search space termed key set, which only contains the key instances required to update the induced rule, to conduct value reduction. The monotonicity of key set ensures the feasibility of our accelerator. Third, a rule-induction accelerator is designed based on key set, and it is theoretically guaranteed to display the same results as the unaccelerated version. Specifically, the rank preservation property of key set ensures consistency between the rule induction achieved by the accelerator and the unaccelerated method. Finally, extensive experiments demonstrate that the proposed accelerator can perform remarkably faster than the unaccelerated rule-based classifier methods, especially on datasets with numerous instances.