通过学习连续时间马尔可夫链反向过程，实现离散分布采样。
Sampling from Energy distributions with Target Concrete Score Identity
- 基于均匀加噪的前向连续时间马尔可夫链，构建逆向采样路径。
- 无需目标分布样本或归一化常数，即可用蒙特卡洛估计得分。
- 适用于统计物理中的离散分布采样，支持自归一化与无偏算法。
我们提出目标明确得分恒等采样器（TCSIS），一种从离散状态空间的未归一化密度中采样的方法，通过学习连续时间马尔可夫链（CTMC）的反向动态实现。该方法基于具有均匀加噪核的前向时间CTMC，依赖于提出的「目标明确得分恒等式」，该恒等式将具体得分（即两状态边际概率之比）与前向均匀扩散核下玻尔兹曼因子期望比值关联起来。这一形式化使我们能够在不需目标分布样本或计算分区函数的情况下，通过蒙特卡洛方法估计具体得分。我们使用神经网络近似具体得分，并提出两种算法：自归一化TCSIS与无偏TCSIS。最终，我们在统计物理问题上验证了TCSIS的有效性。
原文摘要 · Abstract (English)
We introduce the Target Concrete Score Identity Sampler (TCSIS), a method for sampling from unnormalized densities on discrete state spaces by learning the reverse dynamics of a Continuous-Time Markov Chain (CTMC). Our approach builds on a forward in time CTMC with a uniform noising kernel and relies on the proposed Target Concrete Score Identity, which relates the concrete score, the ratio of marginal probabilities of two states, to a ratio of expectations of Boltzmann factors under the forward uniform diffusion kernel. This formulation enables Monte Carlo estimation of the concrete score without requiring samples from the target distribution or computation of the partition function. We approximate the concrete score with a neural network and propose two algorithms: Self-Normalized TCSIS and Unbiased TCSIS. Finally, we demonstrate the effectiveness of TCSIS on problems from statistical physics.
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