论文标题
线性计算复杂性的分数布朗运动的变异推断
Variational inference of fractional Brownian motion with linear computational complexity
论文作者
论文摘要
我们引入了基于仿真的摊销贝叶斯推理方案，以推断随机步行的参数。我们的方法通过无可能的方法了解了步行参数的后验分布。在第一步中，对图形神经网络进行了模拟数据培训，以学习随机步行的优化低维摘要统计信息。在第二步中，可逆神经网络使用变分推断从学习的摘要统计数据中产生参数的后验分布。我们应用我们的方法来从单轨迹推断布朗尼运动模型的参数。摊销推理过程的计算复杂性与轨迹长度线性缩放，其精度尺度类似于在较大长度上绑定的cram {é} r-rao。该方法对位置噪声是强大的，并且比训练期间看到的轨迹更长的轨迹更长。最后，我们适应了该方案，以表明环境中的有限去相关时间可以从单个轨迹中推断出来。
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph neural network is trained on simulated data to learn optimized low-dimensional summary statistics of the random walk. In the second step an invertible neural network generates the posterior distribution of the parameters from the learnt summary statistics using variational inference. We apply our method to infer the parameters of the fractional Brownian motion model from single trajectories. The computational complexity of the amortized inference procedure scales linearly with trajectory length, and its precision scales similarly to the Cram{é}r-Rao bound over a wide range of lengths. The approach is robust to positional noise, and generalizes well to trajectories longer than those seen during training. Finally, we adapt this scheme to show that a finite decorrelation time in the environment can furthermore be inferred from individual trajectories.
