论文标题
通过逆向多核心最佳运输来估计从汇总数据的潜在人口流量
Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport
论文作者
论文摘要
我们研究了估计从总数数据中估计潜在人口流量的问题。当由于隐私问题或测量保真度而无法获得单个轨迹时，就会出现此问题。取而代之的是，在离散时间点上测量了汇总的观测值，以估计各州之间的人口流量。大多数相关研究通过学习时间均匀的马尔可夫过程的过渡参数来解决问题。尽管如此，大多数现实世界中的流量可能会受到各种不确定性（例如交通拥堵和天气状况）的影响。因此，在许多情况下，时间均匀的马尔可夫模型是更复杂的种群流动的近似值。为了避免这种困难，我们诉诸于多 - 距离最佳运输（MOT）公式，该公式可以自然地表示具有约束边缘的聚合观察结果，并根据成本函数编码时间依赖性的过渡矩阵。特别是，我们建议通过学习MOT框架的成本功能来估计从聚合数据的过渡流，这使我们能够捕获随时间变化的动态模式。实验证明了所提出的算法的准确性比估计几个现实世界过渡流的相关方法的精度提高。
We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations are measured over discrete-time points, for estimating the population flows among states. Most related studies tackle the problems by learning the transition parameters of a time-homogeneous Markov process. Nonetheless, most real-world population flows can be influenced by various uncertainties such as traffic jam and weather conditions. Thus, in many cases, a time-homogeneous Markov model is a poor approximation of the much more complex population flows. To circumvent this difficulty, we resort to a multi-marginal optimal transport (MOT) formulation that can naturally represent aggregated observations with constrained marginals, and encode time-dependent transition matrices by the cost functions. In particular, we propose to estimate the transition flows from aggregated data by learning the cost functions of the MOT framework, which enables us to capture time-varying dynamic patterns. The experiments demonstrate the improved accuracy of the proposed algorithms than the related methods in estimating several real-world transition flows.
