路径权重采样：随机轨迹间互信息的精确蒙特卡洛计算
Path Weight Sampling: Exact Monte Carlo Computation of the Mutual Information between Stochastic Trajectories
AI总结：
提出精确蒙特卡洛技术 Path Weight Sampling (PWS)，首次实现对由 master equation 描述的随机系统输入与输出轨迹间互信息的精确计算，并揭示细菌趋化系统中受体簇数量更少、尺寸更大。
摘要：
大多数自然和工程信息处理系统通过随时间变化的信号传输信息。计算信息传输速率或这些信号时间特征中编码的信息，需要输入与输出信号间作为时间函数的互信息，即输入与输出轨迹间的互信息。然而，由于轨迹空间的高维特性，这一计算极其困难，且所有现有技术均需近似。我们提出了一种称为 Path Weight Sampling (PWS) 的精确蒙特卡洛技术，首次使得计算由 master equation 描述的任意随机系统的输入与输出轨迹间互信息成为可能。核心思想是利用 master equation 计算给定输入轨迹下单条输出轨迹的精确条件概率，并通过在轨迹空间进行蒙特卡洛采样平均该概率以获得互信息。我们提出了 PWS 的三种变体，均使用标准随机模拟算法生成轨迹。Direct PWS 是暴力方法；Rosenbluth-Rosenbluth PWS 利用信号轨迹采样与聚合物采样的类比；Thermodynamic Integration PWS 基于轨迹空间中的可逆功计算。PWS 还能计算具有隐藏内部状态及输出到输入反馈系统的输入与输出轨迹间互信息。将 PWS 应用于由 182 个耦合化学反应组成的细菌趋化系统，不仅证明该方案高效，还表明受体簇数量远少于此前认为的数量，而其尺寸远大于此前认为的尺寸。
英文摘要：
Most natural and engineered information-processing systems transmit information via signals that vary in time. Computing the information transmission rate or the information encoded in the temporal characteristics of these signals, requires the mutual information between the input and output signals as a function of time, i.e. between the input and output trajectories. Yet, this is notoriously difficult because of the high-dimensional nature of the trajectory space, and all existing techniques require approximations. We present an exact Monte Carlo technique called Path Weight Sampling (PWS) that, for the first time, makes it possible to compute the mutual information between input and output trajectories for any stochastic system that is described by a master equation. The principal idea is to use the master equation to evaluate the exact conditional probability of an individual output trajectory for a given input trajectory, and average this via Monte Carlo sampling in trajectory space to obtain the mutual information. We present three variants of PWS, which all generate the trajectories using the standard stochastic simulation algorithm. While Direct PWS is a brute-force method, Rosenbluth-Rosenbluth PWS exploits the analogy between signal trajectory sampling and polymer sampling, and Thermodynamic Integration PWS is based on a reversible work calculation in trajectory space. PWS also makes it possible to compute the mutual information between input and output trajectories for systems with hidden internal states as well as systems with feedback from output to input. Applying PWS to the bacterial chemotaxis system, consisting of 182 coupled chemical reactions, demonstrates not only that the scheme is highly efficient, but also that the number of receptor clusters is much smaller than hitherto believed, while their size is much larger.
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。
