通过联合降维加速最优分类树计算,显著提升大规模数据处理效率。
Scaling Optimal Classification Trees via Adaptive Feature and Sample Reduction

- 基于STreeD框架,动态合并重复样本并保留特征,减少计算开销。
- 自适应迭代优化候选集,在深度2-4时提速超120倍,深度更大时仍可生成可行解。
- 适合需要高效构建最优决策树的科研与工业场景,尤其在资源受限时表现优异。
动态规划求解最优分类树随特征和样本数量增加而变得计算昂贵。本文提出基于STreeD的联合特征与样本空间缩减框架。加权STreeD将投影到固定候选集后的重复记录合并为加权代表,降低样本相关计算量而不改变优化问题。自适应STreeD反复精炼有限候选集,保留当前树使用的特征,重建加权表示并求解简化问题。每个加权STreeD解均针对当前候选集最优,外层特征搜索仍为全特征空间上的启发式方法。在五个数据集上实验表明,加权STreeD相比标准STreeD最快提速121.41倍;自适应STreeD在深度2至4的对比中显著缩短运行时间,并在更深层仍能生成可行解,而全特征方法因时间和内存限制无法求解。相同计算预算下,其预测性能与基准最优分类树相当,部分情况下更优。结果表明,联合特征与样本空间缩减可有效扩展动态规划类最优树学习至更具挑战性的实例。
原文摘要 · Abstract (English)
Dynamic programming for optimal classification trees becomes computationally expensive as the numbers of features and training samples increase. We develop a joint feature- and sample-space reduction framework based on STreeD. Weighted STreeD merges duplicate records created after projection onto a fixed candidate set into weighted representatives. This reduces sample-dependent computation without changing the fixed-candidate optimization problem. Adaptive STreeD repeatedly refines a bounded candidate set, retains features used by the incumbent tree, rebuilds the weighted representation, and solves the resulting reduced problems. Each certified Weighted STreeD solution is optimal for its current candidate set, while the outer feature search remains heuristic over the full feature space. Experiments on five data sets show that Weighted STreeD achieves speedups of up to 121.41 times over standard STreeD. Adaptive STreeD reduces runtime in matched comparisons at depths 2 to 4 and continues to return feasible trees at greater depths where full-feature methods are limited by time or memory. Under the same computational budget, its predictive performance remains comparable to the evaluated optimal classification tree baselines and is higher in some comparisons. These results show how joint feature- and sample-space reduction can scale dynamic-programming-based optimal-tree learning to more demanding instances.
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