发表机构
Duke University（杜克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对强凸光滑目标分布，提出弹跳粒子采样器与Zigzag采样器的窗口化减薄精确模拟方法，推导得到两类采样器的高斯冷启动下的查询复杂度上界。
AI 中文摘要
设μ(dx)∝e^{-U(x)}dx定义在R^d上，其中U为m强凸且L光滑，记条件数κ=L/m。研究窗口化减薄这一弹跳粒子采样器和坐标Zigzag过程的精确模拟方法，该方法将轨迹划分为确定性窗口，利用每个窗口起始处的梯度评估构造事件率的易处理局部包络。结合该构造、定量混合估计及弹跳与翻转期望次数的有限时间界，得到高斯冷启动下的查询复杂度保证：对于总变差误差ε，弹跳粒子采样器的期望查询次数为O(κ^{1/2}d(d log κ + log 1/ε))梯度查询；Zigzag采样器的期望查询次数为O(κ d^{1/4}(d log κ + log 1/ε))全梯度当量，其中d个坐标偏导数查询计为1个当量。
英文摘要
Let $μ(d x)\propto e^{-U(x)} d x$ on $\R^d$, where $U$ is $m$-strongly convex and $L$-smooth, and denote by $κ=L/m$ the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start. For total-variation error $\varepsilon$, the expected query counts are $O(κ^{1/2}d\,(d\logκ+\log\frac1\varepsilon))$ gradient queries for the bouncy particle sampler and $O(κd^{1/4}(d\logκ+\log\frac1\varepsilon))$ full-gradient equivalents for Zigzag, where $d$ coordinate-partial queries count as one equivalent.
Commentsv2: corrected a few typos and updated references
