Change point estimation is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidates requires $O(n)$ evaluations of the gain function for an interval with $n$ observations. If each evaluation is computationally demanding (e.g. in high-dimensional models), this can become infeasible. Instead, we propose optimistic search methods with $O(\log n)$ evaluations exploiting specific structure of the gain function. Towards solid understanding of our strategy, we investigate in detail the $p$-dimensional Gaussian changing means setup, including high-dimensional scenarios. For some of our proposals, we prove asymptotic minimax optimality for detecting change points and derive their asymptotic localization rate. These rates (up to a possible log factor) are optimal for the univariate and multivariate scenarios, and are by far the fastest in the literature under the weakest possible detection condition on the signal-to-noise ratio in the high-dimensional scenario. Computationally, our proposed methodology has the worst case complexity of $O(np)$, which can be improved to be sublinear in $n$ if some a-priori knowledge on the length of the shortest segment is available. Our search strategies generalize far beyond the theoretically analyzed setup. We illustrate, as an example, massive computational speedup in change point detection for high-dimensional Gaussian graphical models.

翻译：切换点估计通常是为了寻找最大增益函数, 描述在数据分割时更适合的数据。 搜索所有候选人都需要用美元( n) 来对增益函数进行评估, 间隔时间为 $n 。 如果每次评估都计算要求很高( 如在高维模型中), 就可能变得不可行。 相反, 我们提出乐观搜索方法, 使用美元( log n) 来利用增益功能的具体结构。 为了对战略有扎实的理解, 我们详细调查了美元( 美元) 的维度测量变化手段设置, 包括高维度假设。 对于我们的一些提案, 我们证明在探测变化点和得出无损本地本地化率时, 需要略微小的微优化。 这些比率( 可能达到一个逻辑系数) 最符合单向和多变量假设情景的最佳搜索方法, 在高维度假设情况下, 我们的拟议方法最差的 美元( nprialalal) 比例是最短的搜索方法, 以最短的案例复杂性为 $ (nprial prial descrial) sealal seal squistration a prial sal requistration a pal pal seal pal pregrealtime a pal a pal pal pal pal pal laglegleglegal a pal pal) a pal a pal a pal a pal se a pal a pal a pal a pal a seal se a pal a preal sealtimental a pal a pal a pal a pal a pal a pal se.