论文标题
使用蒙特卡洛估计得分和甲骨文访问目标密度的基于得分的方法的提议进行抽样方法
Proposal of a Score Based Approach to Sampling Using Monte Carlo Estimation of Score and Oracle Access to Target Density
论文作者
论文摘要
作为生成算法，基于得分的采样方法已经取得了很大的成功，以从目标密度产生新的样品给定初始样品池。在这项工作中，我们考虑是否没有目标密度的初始样本，而是$ 0^{th} $和$ 1^{st} $ oracle Oracle访问日志可能性。贝叶斯后采样或非凸函数的近似最小化可能出现此类问题。我们仅利用这些知识，就提出了一种蒙特卡洛方法，以经验估算得分作为对随机变量的特定期望。然后，使用此估算器，我们可以运行向后流SDE的离散版本以从目标密度产生样品。这种方法的好处是不依赖目标密度的初始样品池，并且它不依赖神经网络或其他黑匣子模型来估计分数。
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.
