用最优传输方法完成分布矩阵补全，提升预测精度。
Distributional Matrix Completion via Nearest Neighbors in the Wasserstein Space
- 基于最优传输的最近邻法扩展到分布数据补全
- 在真实数据上显著优于仅用观测样本的估计
- 适合处理异方差分布，适用于金融等场景
我们研究分布矩阵补全问题：给定一个稀疏观测的分布矩阵，目标是推断出所有已观测和未观测条目的真实分布。这是传统矩阵补全（每条目为标量）的推广。本文利用最优传输工具，将最近邻方法推广至分布情形。在概率分布的潜在因子模型下，证明该方法能在Wasserstein度量下恢复真实分布。模拟实验表明，该方法（i）相比仅使用某条目观测样本，能提供更优的分布估计；（ii）可准确估计标准差、风险价值（Value-at-Risk）等分布统计量；（iii）天然支持异方差分布。此外，在季度收益预测分布的真实数据集上验证了方法有效性。还证明了关于一维分布Wasserstein中位数的新渐近结果。
原文摘要 · Abstract (English)
We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a generalization of traditional matrix completion, where the observations per matrix entry are scalar-valued. To do so, we utilize tools from optimal transport to generalize the nearest neighbors method to the distributional setting. Under a suitable latent factor model on probability distributions, we establish that our method recovers the distributions in the Wasserstein metric. We demonstrate through simulations that our method (i) provides better distributional estimates for an entry compared to using observed samples for that entry alone, (ii) yields accurate estimates of distributional quantities such as standard deviation and value-at-risk, and (iii) inherently supports heteroscedastic distributions. In addition, we demonstrate our method on a real-world dataset of quarterly earnings prediction distributions. We also prove novel asymptotic results for Wasserstein barycenters over one-dimensional distributions.
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。