Liang Cao

Jiayang Ren, Valentín Osuna-Enciso, Morimasa Okamoto et al.

Decision trees are essential yet NP-complete to train, prompting the widespread use of heuristic methods such as CART, which suffers from sub-optimal performance due to its greedy nature. Recently, breakthroughs in finding optimal decision trees have emerged; however, these methods still face significant computational costs and struggle with continuous features in large-scale datasets and deep trees. To address these limitations, we introduce a moving-horizon differential evolution algorithm for classification trees with continuous features (MH-DEOCT). Our approach consists of a discrete tree decoding method that eliminates duplicated searches between adjacent samples, a GPU-accelerated implementation that significantly reduces running time, and a moving-horizon strategy that iteratively trains shallow subtrees at each node to balance the vision and optimizer capability. Comprehensive studies on 68 UCI datasets demonstrate that our approach outperforms the heuristic method CART on training and testing accuracy by an average of 3.44% and 1.71%, respectively. Moreover, these numerical studies empirically demonstrate that MH-DEOCT achieves near-optimal performance (only 0.38% and 0.06% worse than the global optimal method on training and testing, respectively), while it offers remarkable scalability for deep trees (e.g., depth=8) and large-scale datasets (e.g., ten million samples).

Yang Liu, Jing Liu, Chengfang Li et al.

Anomaly detection (AD) plays a pivotal role across diverse domains, including cybersecurity, finance, healthcare, and industrial manufacturing, by identifying unexpected patterns that deviate from established norms in real-world data. Recent advancements in deep learning, specifically diffusion models (DMs), have sparked significant interest due to their ability to learn complex data distributions and generate high-fidelity samples, offering a robust framework for unsupervised AD. In this survey, we comprehensively review anomaly detection and generation with diffusion models (ADGDM), presenting a tutorial-style analysis of the theoretical foundations and practical implementations and spanning images, videos, time series, tabular, and multimodal data. Crucially, unlike existing surveys that often treat anomaly detection and generation as separate problems, we highlight their inherent synergistic relationship. We reveal how DMs enable a reinforcing cycle where generation techniques directly address the fundamental challenge of anomaly data scarcity, while detection methods provide critical feedback to improve generation fidelity and relevance, advancing both capabilities beyond their individual potential. A detailed taxonomy categorizes ADGDM methods based on anomaly scoring mechanisms, conditioning strategies, and architectural designs, analyzing their strengths and limitations. We final discuss key challenges including scalability and computational efficiency, and outline promising future directions such as efficient architectures, conditioning strategies, and integration with foundation models (e.g., visual-language models and large language models). By synthesizing recent advances and outlining open research questions, this survey aims to guide researchers and practitioners in leveraging DMs for innovative AD solutions across diverse applications.