Abstract: The feature space of feature inheritance data streams evolves over time with new features being added and old features partially disappearing while others are inherited and retained. This dynamic nature limits the effectiveness of traditional data stream classification methods. Although second-order online learning methods have shown strong predictive performance in previous data stream classification tasks, they are challenging to apply directly to scenarios with dynamic feature changes and are computationally expensive. To address these issues, an online learning method for feature inheritance data streams is proposed. First, second-order online learning models with adaptive weight regularization are constructed for disappearing and inherited features. To enhance training efficiency, Bernoulli sampling is used to select data samples near the decision boundary for model training. Second, new classification models are established for newly added features, and the predictive information from models on disappearing and inherited features is utilized to accelerate model optimization. Finally, to further improve predictive performance, a dynamic weighted ensemble strategy is employed to achieve joint prediction from models on inherited and newly added features. Extensive simulation experiments demonstrate that our method improves classification accuracy by an average of 4.6% compared to baseline methods, while reducing model update frequency and enhancing prediction precision, thereby validating the effectiveness of our approach.