Introduction:
Computer simulations of complex systems are vital in many fields, such as economics and engineering. However, simulations of multi-modal distributions can be expensive and prone to error, which can lead to unreliable predictions. To address this issue, researchers have proposed a novel method of sampling from a flattened distribution to speed up computations and estimate the importance weights between the original distribution and the flattened distribution to ensure the accuracy
Metropolis-Hastings is an important algorithm for approximate inference in statistics. It is a Markov Chain Monte Carlo (MCMC) algorithm that allows for sampling from a probability distribution where direct sampling is difficult due to the presence of an intractable integral.
How Metropolis-Hastings works
Metropolis-Hastings consists of a proposal distribution to draw a parameter value. This is denoted as q(θ’|θ). To decide whether θ’ is accepted or rejected, we then calculate a ratio of:
$$
reSGLD, or Rescaled Stochastic Gradient Langevin Dynamics, is an algorithm used in machine learning to optimize the performance of models by efficiently exploring and exploiting different feature spaces. It involves simulating two types of particles, high-temperature and low-temperature particles, and swapping them simultaneously to achieve better optimization results.
Understanding reSGLD
In machine learning, the goal is to optimize models to achieve the best possible performance. This optim