DUST：一种基于对偶性的精确多重变点检测剪枝方法
DUST: A Duality-Based Pruning Method For Exact Multiple Change-Point Detection
AI总结：
针对现有变点检测剪枝方法PELT和FPOP的局限，提出基于对偶性的DUST框架，通过评估对偶函数阈值剪枝候选变点，适用于任意维度参数模型，在保持精确性的同时显著提升计算效率。
摘要：
我们通过优化源自指数族模型的惩罚似然，解决了在大型时间序列中检测多个变点的挑战。动态规划算法能以至多二次时间复杂度精确求解此任务。近年来，剪枝策略的发展大幅提升了其计算效率。然而，现有两种方法存在显著局限：PELT在稀疏变化场景下剪枝效率不佳，而FPOP的结构不适用于多参数设置。为解决这些问题，我们提出了DUal Simple Test（DUST）框架，通过评估对偶函数与阈值的对比来剪枝候选变点。该方法高度灵活，广泛适用于任意维度的参数模型。在温和假设下，我们为底层非凸剪枝问题建立了强对偶性。我们展示了DUST在各种变点机制和模型中的有效性。特别地，对于单参数模型，DUST兼具PELT的简洁性与FPOP的高效性。其应用对非高斯模型尤为有利。最后，我们将DUST应用于方差变化模型下的小鼠监测时间序列，展示了其高效恢复最优变点结构的能力。
英文摘要：
We tackle the challenge of detecting multiple change points in large time series by optimising a penalised likelihood derived from exponential family models. Dynamic programming algorithms can solve this task exactly with at most quadratic time complexity. In recent years, the development of pruning strategies has drastically improved their computational efficiency. However, the two existing approaches have notable limitations: PELT struggles with pruning efficiency in sparse-change scenarios, while FPOP's structure is not adapted to multi-parametric settings. To address these issues, we introduce the DUal Simple Test (DUST) framework, which prunes candidate changes by evaluating a dual function against a threshold. This approach is highly flexible and broadly applicable to parametric models of any dimension. Under mild assumptions, we establish strong duality for the underlying non-convex pruning problem. We demonstrate DUST's effectiveness across various change-point regimes and models. In particular, for one-parametric models, DUST matches the simplicity of PELT with the efficiency of FPOP. Its use is especially advantageous for non-Gaussian models. Finally, we apply DUST to mouse monitoring time series under a change-in-variance model, illustrating its ability to recover the optimal change-point structure efficiently.
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