Title: Score Matching With Missing Data Show Chinese title

Title: 带缺失数据的匹配评分

Abstract: Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work explores its use when data is incomplete. We address this by adapting score matching (and its major extensions) to work with missing data in a flexible setting where data can be partially missing over any subset of the coordinates. We provide two separate score matching variations for general use, an importance weighting (IW) approach, and a variational approach. We provide finite sample bounds for our IW approach in finite domain settings and show it to have especially strong performance in small sample lower dimensional cases. Complementing this, we show our variational approach to be strongest in more complex high-dimensional settings which we demonstrate on graphical model estimation tasks on both real and simulated data. Show Chinese abstract

Abstract: 得分匹配是一种用于学习数据分布的重要工具，在扩散过程、基于能量的建模和图形模型估计等多个领域均有应用。 尽管有这些广泛应用，却很少有研究探索得分匹配在数据不完整时的使用。 我们通过调整得分匹配（及其主要扩展形式）来解决这一问题，使其能够在数据部分缺失于任意坐标子集的情况下灵活处理缺失数据。 我们提供了两种通用的得分匹配变体：重要性加权（IW）方法和变分方法。 我们在有限域设置下为我们的IW方法提供了有限样本界，并表明它在小样本低维情况下表现出色。 与此互补，我们证明了变分方法在更复杂的高维设置中表现最佳，这在真实和模拟数据的图形模型估计任务中得到了验证。