Mean Field Initialization of the Annealed Importance Sampling Algorithm for an Efficient Evaluation of the Partition...

Area of Science:

• Statistical physics
• Machine learning
• Computational physics

Background:

• Probabilistic models in physics necessitate calculating partition functions (Z), which is computationally intensive for large systems.
• Annealed Importance Sampling (AIS) offers a stochastic method for estimating Z, particularly suitable for parallel implementation in Restricted Boltzmann Machines (RBMs).

Purpose of the Study:

• To evaluate the partition function (Z) of magnetic spin systems using AIS within RBMs.
• To enhance the efficiency and accuracy of AIS by optimizing the starting probability distribution.

Main Methods:

• Applied AIS to estimate the partition function (Z) for magnetic spin and spin-like systems mapped to RBMs.
• Investigated the impact of using a mean-field starting probability distribution compared to the standard uniform distribution.
• Conducted systematic analyses on small and large systems, comparing results with known exact values.

Main Results:

• A properly selected mean-field starting distribution significantly improves the quality of Z estimation and reduces computational cost.
• Two successful strategies for using mean-field distributions with AIS were identified and validated across various problem sizes.
• The proposed methods provide reliable Z estimations with reduced computational expense, independent of any learning process or training data.

Conclusions:

• Optimized starting distributions, specifically mean-field ones, enhance AIS performance for partition function estimation in RBMs.
• The presented strategies offer efficient and accurate methods for estimating partition functions, applicable to magnetic systems without requiring prior training data.
• This work provides practical improvements for applying AIS in computational physics and machine learning contexts.