Proposal of a Score Based Approach to Sampling Using Monte Carlo Estimation of Score and Oracle Access to Target Density
This addresses sampling challenges in Bayesian posterior inference and non-convex optimization, offering a method that avoids reliance on initial samples or neural networks, though it is incremental as it builds on existing score-based approaches.
The paper tackles the problem of sampling from a target density without initial samples by proposing a Monte Carlo method to estimate the score using oracle access to the log likelihood, enabling sample generation via a backward flow SDE.
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target density, but rather $0^{th}$ and $1^{st}$ order oracle access to the log likelihood. Such problems may arise in Bayesian posterior sampling, or in approximate minimization of non-convex functions. Using this knowledge alone, we propose a Monte Carlo method to estimate the score empirically as a particular expectation of a random variable. Using this estimator, we can then run a discrete version of the backward flow SDE to produce samples from the target density. This approach has the benefit of not relying on a pool of initial samples from the target density, and it does not rely on a neural network or other black box model to estimate the score.