用神经网络建模随机预条件矩阵，提升高维多峰密度采样效率
Neural Network Approach to Stochastic Dynamics for Smooth Multimodal Density Estimation
- 将预条件矩阵设为随机矩阵，仅需后验梯度信息
- 在平面自由粒子量子概率密度上实现更高精度与更快计算速度
- 适合需要高效采样的高维复杂分布建模任务
本文提出一种基于Langevin扩散动力学的新概率采样方法，解决传统蒙特卡洛算法在高维目标密度采样中的瓶颈。通过将预条件矩阵的随机性建模为随机矩阵，扩展了马尔可夫调整Langevin扩散算法。该方法仅需后验对数梯度，具备完全自适应机制，能有效捕捉统计模型的局部几何结构。在平面自由粒子的量子概率密度函数（能量本征函数）建模中验证了其优势，相比标准MCMC方法，在性能准确性和计算时间上均有显著提升。
原文摘要 · Abstract (English)
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent Metropolis-Adjusted Langevin Diffusion algorithm by modelling the stochasticity of precondition matrix as a random matrix. An advantage compared to other proposal method is that it only requires the gradient of log-posterior. The proposed method provides fully adaptation mechanisms to tune proposal densities to exploits and adapts the geometry of local structures of statistical models. We clarify the benefits of the new proposal by modelling a Quantum Probability Density Functions of a free particle in a plane (energy Eigen-functions). The proposed model represents a remarkable improvement in terms of performance accuracy and computational time over standard MCMC method.
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