Adaptive Loss Weighting

The design of learning objectives is central to training time-series forecasting models. Existing learning objectives such as mean squared error mostly treat each future step as an independent, equally weighted task, which leads to the following two challenges: (1) they overlook the label autocorrelation effect among future steps, leading to biased learning objectives; (2) they fail to set heterogeneous task weights for different forecasting tasks corresponding to varying future steps, limiting the forecasting performance. To fill this gap, we propose a novel quadratic-form weighted learning objective, addressing both issues simultaneously. Specifically, the off-diagonal elements of the weighting matrix account for the label autocorrelation effect, whereas the non-uniform diagonals are expected to match the preferred weights of the forecasting tasks with varying future steps. On this basis, we propose a Quadratic Direct Forecast (QDF) learning algorithm, which trains the forecast model using the adaptively updated quadratic-form weighting matrix. Experiments show that our QDF effectively improves the performance of various forecast models, achieving state-of-the-art results. Code is available at https://github.com/Master-PLC/QDF.

Class imbalance poses a significant challenge in classification tasks, often causing standard learning algorithms to become biased toward the majority class. Cost-sensitive learning (CSL) addresses this issue by assigning higher penalties to minority-class misclassifications. However, conventional CSL typically applies a uniform penalty to all minority-class instances, ignoring the fact that minority samples may differ substantially in terms of local safety, overlap, boundary ambiguity, and outlier-like behavior. Uniform penalization can therefore introduce undue bias, increasing the number of misclassifications. In this study, we propose iCost, an instance-complexity-aware CSL framework that assigns adaptive penalties to minority-class samples according to their estimated learning difficulty. This fine-grained penalization strategy ensures fairer weighting, reduces unwarranted bias, and improves overall classification performance. Two complementary complexity estimation strategies are introduced: Neighbor-iCost, based on local neighborhood composition, and Gini-iCost, based on Gini-impurity-based feature-space partitioning. Extensive experiments on 65 binary and 10 multiclass imbalanced datasets show that iCost outperforms conventional CSL by a clear margin and remains highly competitive with widely used resampling methods. To support reproducibility and practical adoption, the proposed algorithm has been released as a scikit-learn-compatible Python package through PyPI. This work offers a fresh perspective on imbalanced learning by integrating instance-level data complexity into the learning process, opening new avenues for developing adaptive, complexity-aware strategies for imbalanced classification.