贪心泊松拒绝采样
Greedy Poisson Rejection Sampling
AI总结：
本文提出贪心泊松拒绝采样（GPRS），通过将拒绝采样等价于对泊松过程点的贪心搜索，在一维单峰密度比问题中实现最优运行时间的单次信道模拟，并实验证明其显著优于 A* coding。
摘要：
单次信道模拟是一个基础的数据压缩问题，关注的是使用编码分布 $P$ 以尽可能少的平均比特数对来自目标分布 $Q$ 的单个样本进行编码。解决该问题的算法在神经数据压缩和差分隐私中具有应用，并且可以作为基于量化方法的更高效替代方案。遗憾的是，现有解决方案要么速度过慢，要么适用范围有限，阻碍了其广泛采用。在本文中，我们通过描述一种具有最优运行时间的算法，最终解决了目标-提议密度比为单峰的一维问题中的单次信道模拟。我们通过构造一个拒绝采样过程来实现这一点，该过程等价于在泊松过程的点上进行贪心搜索。因此，我们将该算法称为贪心泊松拒绝采样（GPRS），并分析了其若干变体的正确性和时间复杂度。最后，我们通过实验验证了我们的定理，证明 GPRS 显著优于当前最先进的方法 A* coding。我们的代码可在 https://github.com/gergely-flamich/greedy-poisson-rejection-sampling 获取。
英文摘要：
One-shot channel simulation is a fundamental data compression problem concerned with encoding a single sample from a target distribution $Q$ using a coding distribution $P$ using as few bits as possible on average. Algorithms that solve this problem find applications in neural data compression and differential privacy and can serve as a more efficient alternative to quantization-based methods. Sadly, existing solutions are too slow or have limited applicability, preventing widespread adoption. In this paper, we conclusively solve one-shot channel simulation for one-dimensional problems where the target-proposal density ratio is unimodal by describing an algorithm with optimal runtime. We achieve this by constructing a rejection sampling procedure equivalent to greedily searching over the points of a Poisson process. Hence, we call our algorithm greedy Poisson rejection sampling (GPRS) and analyze the correctness and time complexity of several of its variants. Finally, we empirically verify our theorems, demonstrating that GPRS significantly outperforms the current state-of-the-art method, A* coding. Our code is available at https://github.com/gergely-flamich/greedy-poisson-rejection-sampling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
