We introduce smallest valid partitioning (SVP), a segmentation method for multiple change-point detection in time-series. SVP relies on a local notion of segment validity: a candidate segment is retained only if it passes a user-chosen validity test (e.g., a single change-point test). From the collection of valid segments, we propose a coherent aggregation procedure that constructs a global segmentation which is the exact solution of an optimization problem. Our main contribution is the use of a lexicographic order for the optimization problem that prioritizes parsimony. We analyze the computational complexity of the resulting procedure, which ranges from linear to cubic time depending on the chosen cost and validity functions, the data regime and the number of detected changes. Finally, we assess the quality of SVP through comparisons with standard optimal partitioning algorithms, showing that SVP yields competitive segmentations while explicitly enforcing segment validity. The flexibility of SVP makes it applicable to a broad class of problems; as an illustration, we demonstrate robust change-point detection by encoding robustness in the validity criterion.

翻译：本文提出最小有效划分（SVP）方法，用于时间序列中的多变化点检测。SVP基于一种局部化的段有效性概念：仅当候选段通过用户选定的有效性检验（例如单变化点检验）时才会被保留。从有效段的集合出发，我们提出一种一致性聚合流程，构建出作为优化问题精确解的全局划分方案。我们的核心贡献在于采用字典序优化准则，优先保证划分的简约性。我们分析了该方法的计算复杂度，其范围从线性到三次方时间不等，具体取决于所选成本函数与有效性函数、数据状态以及检测到的变化点数量。最后，通过与标准最优划分算法的比较评估SVP的效能，结果表明SVP在明确保证段有效性的同时，能够生成具有竞争力的划分方案。SVP的灵活性使其适用于广泛的问题类别；作为示例，我们通过在有效性准则中嵌入鲁棒性编码，展示了鲁棒变化点检测的实现。