论文标题
Bézier插值从数据中提高了动态模型的推断
Bézier interpolation improves the inference of dynamical models from data
论文作者
论文摘要
从量子多体系统到不断发展的人口到金融市场的许多动力系统都通过随机过程来描述。通常可以使用在随机路径上集成的信息来推断表征此类过程的参数。但是，从有限时间分辨率的实际数据中估算时间融合的数量是有挑战性的。在这里，我们提出了一个框架，用于使用Bézier插值准确估算时间集成数量。我们将方法应用于两个动态推理问题：确定不断发展的人群的适应性参数和推断驱动Ornstein-Uhlenbeck过程的力量。我们发现，贝齐尔插值减少了两个动态推断问题的估计偏差。对于时间有限的数据集，这种改进尤其明显。我们的方法可以广泛应用，以提高使用有限采样数据的其他动态推理问题的准确性。
Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over stochastic paths. However, estimating time-integrated quantities from real data with limited time resolution is challenging. Here, we propose a framework for accurately estimating time-integrated quantities using Bézier interpolation. We applied our approach to two dynamical inference problems: determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes. We found that Bézier interpolation reduces the estimation bias for both dynamical inference problems. This improvement was especially noticeable for data sets with limited time resolution. Our method could be broadly applied to improve accuracy for other dynamical inference problems using finitely sampled data.
