Neural Network Approach to Stochastic Dynamics for Smooth Multimodal Density Estimation
This provides an incremental improvement for researchers needing efficient sampling in high-dimensional statistical models, particularly in quantum physics applications.
The authors tackled the problem of sampling from high-dimensional multimodal densities by extending the Metropolis-Adjusted Langevin Diffusion algorithm with a random precondition matrix, requiring only gradient information. Their method showed improved performance accuracy and computational time over standard MCMC when tested on quantum probability density functions.
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.