通过插值进行推断：对比表示可证明地支持规划与推断
Inference via Interpolation: Contrastive Representations Provably Enable Planning and Inference
AI总结：
针对高维时间序列的概率推断难题，提出将对比学习变体应用于时间序列，证明其学到的表示遵循高斯-马尔可夫链，推断可转化为低维矩阵求逆，特殊情形下等价于表示插值，并通过46维内的数值模拟验证了理论。
摘要：
给定时间序列数据，我们如何回答“未来会发生什么？”以及“我们是如何走到这一步的？”这类问题？当观测数据是高维的时，这类概率推断问题极具挑战性。本文中，我们展示了如何借助学习到的表示，得到这些问题的紧致闭式解。核心思路是将一种对比学习变体应用于时间序列数据。已有研究表明，对比学习学到的表示编码了概率比。我们拓展了已有工作，证明表示上的边缘分布是高斯分布，进而可证明表示的联合分布也是高斯分布。综合这些结果，时间对比学习学到的表示遵循高斯-马尔可夫链——这是一种图模型，在该模型中，对表示的推断（如预测、规划）等价于对低维矩阵求逆。在一种特殊情形下，推断中间表示等价于在已学习的表示之间进行插值。我们通过最高达46维任务的数值模拟验证了我们的理论。
英文摘要：
Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
