Free Energy Evaluation Using Marginalized Annealed Importance Sampling
arXiv:2204.03784 · doi:10.1103/PhysRevE.106.024127
Abstract
The evaluation of the free energy of a stochastic model is considered a significant issue in various fields of physics and machine learning. However, the exact free energy evaluation is computationally infeasible because the free energy expression includes an intractable partition function. Annealed importance sampling (AIS) is a type of importance sampling based on the Markov chain Monte Carlo method that is similar to a simulated annealing and can effectively approximate the free energy. This study proposes an AIS-based approach, which is referred to as marginalized AIS (mAIS). The statistical efficiency of mAIS is investigated in detail based on theoretical and numerical perspectives. Based on the investigation, it is proved that mAIS is more effective than AIS under a certain condition.
References in corpus (11)
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
- Many-body quantum state tomography with neural networks
- Equivalence of restricted Boltzmann machines and tensor network states
- Statistical physics of pairwise probability models
- Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
- Restricted Boltzmann Machine, recent advances and mean-field theory
- Stochastic normalizing flows as non-equilibrium transformations
- Barriers and Dynamical Paths in Alternating Gibbs Sampling of Restricted Boltzmann Machines
- A Generalization of Spatial Monte Carlo Integration
- Spatial Monte Carlo Integration with Annealed Importance Sampling