论文标题
通过deno的自动编码器和Langevin采样的生成建模
Generative Modeling with Denoising Auto-Encoders and Langevin Sampling
论文作者
论文摘要
我们研究了一种生成建模方法的收敛性，该方法首先使用Denoising自动编码器（DAE）或Denoising评分匹配（DSM）估算分布的得分函数，然后采用Langevin扩散进行抽样。我们表明，DAE和DSM均提供了高斯平滑种群密度分数的估计，从而使我们能够应用经验过程的机制。 我们克服了仅依靠$ l^2 $界限的分数估计误差的挑战，并在人口分布法和该采样方案的法律之间提供有限样本界限。然后，我们将结果应用于Arxiv的同型方法：1907.05600，并为其经验成功提供了理论上的理由。
We study convergence of a generative modeling method that first estimates the score function of the distribution using Denoising Auto-Encoders (DAE) or Denoising Score Matching (DSM) and then employs Langevin diffusion for sampling. We show that both DAE and DSM provide estimates of the score of the Gaussian smoothed population density, allowing us to apply the machinery of Empirical Processes. We overcome the challenge of relying only on $L^2$ bounds on the score estimation error and provide finite-sample bounds in the Wasserstein distance between the law of the population distribution and the law of this sampling scheme. We then apply our results to the homotopy method of arXiv:1907.05600 and provide theoretical justification for its empirical success.
