用确定性流方法改进采样与推断，解决密度估计难题
Deterministic Fokker-Planck Transport -- With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlo
- 基于福克-普朗克方程构造确定性粒子流，避免密度直接计算
- 在变分推断等场景中，密度估计误差反而提升算法性能
- 适合做采样、变分推断和序列蒙特卡洛的高精度建模
福克-普朗克方程可重写为连续性方程，自然引出使用关联速度场的粒子流方法。尽管由此产生的概率流微分方程具有优良性质——如作为目标分布与当前分布间相对熵关于2-沃瑟斯坦距离的梯度流——但其依赖于对当前概率密度的评估，这在大多数实际应用中不可行。通过深入分析基于核密度估计近似该密度的缺陷，我们发现这些局限在变分推断、核均值嵌入及序列蒙特卡洛等场景中可转化为优势。
原文摘要 · Abstract (English)
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing properties - such as defining a gradient flow of the Kullback-Leibler divergence between the current and target densities with respect to the 2-Wasserstein distance - it relies on evaluating the current probability density, which is intractable in most practical applications. By closely examining the drawbacks of approximating this density via kernel density estimation, we uncover opportunities to turn these limitations into advantages in contexts such as variational inference, kernel mean embeddings, and sequential Monte Carlo.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。