We present a novel lightweight incremental quantile estimator which possesses far less complexity than the Tierney’s estimator and its extensions. Notably, our algorithm relies only on tuning one single parameter which is a plausible property which we could only find in the discretized quantile estimator Frugal. This makes our algorithm easy to tune for better performance. Furthermore, our algorithm is multiplicative which makes it highly suitable to handle quantile estimation in systems in which the underlying distribution varies with time. Unlike Frugal and our legacy work which are randomized algorithms, we suggest deterministic updates where the step size is adjusted in a subtle manner to ensure the convergence. The deterministic algorithm is more efficient since the estimate is updated at every iteration. The convergence of the proposed estimator is proven using the theory of stochastic learning. Extensive experimental results show that our estimator clearly outperforms legacy works.

中文翻译：

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增量分位数估计的乘性更新方法

我们提出了一种新颖的轻量级增量分位数估计器，其复杂度远低于Tierney的估计器及其扩展。值得注意的是，我们的算法仅依赖于调整单个参数，这是一个合理的属性，我们只能在离散分位数估计器Frugal中找到。这使得我们的算法易于调整以获得更好的性能。此外，我们的算法是可乘的，这使其非常适合处理基础分布随时间变化的系统中的分位数估计。与作为随机算法的Frugal和我们的传统工作不同，我们建议进行确定性更新，以微妙的方式调整步长以确保收敛。确定性算法效率更高，因为估算值在每次迭代时都会更新。利用随机学习理论证明了所提出估计量的收敛性。大量的实验结果表明，我们的估算器明显优于传统作品。