高斯过程潜变量模型的摊销结构化随机变分推断

中文摘要 AI 辅助

许多机器学习方法旨在近似数据所在的低维流形。这类方法的一个理想特性是能够捕获所学流形的认知不确定性。高斯过程潜变量模型实现了这一目标，其中从潜空间到观测空间的高斯过程（GP）映射提供了流形不确定性的估计。然而，这种不确定性估计的有效性受到GP诱导点与潜变量之间的平均场变分近似的限制。在本工作中，我们应用摊销结构化随机变分推断，使潜空间的变分后验条件依赖于诱导点的值。我们证明，这种更灵活的变分后验改善了与数据流形上点重建相关的多项指标。

英文摘要

Many machine learning methods aim to approximate the lower-dimensional manifold on which the data lives. A desirable feature of such methods is that they should capture the epistemic uncertainty of this learned manifold. One model that achieves this is the Gaussian Process Latent Variable Model, in which a Gaussian Process (GP) mapping from the latent space provides an estimate of the uncertainty of the manifold. However, the effectiveness of this uncertainty estimation is limited by the mean-field variational approximation between the GP inducing points and the latent variables. In this work, we apply Amortized Structured Stochastic Variational Inference to allow the variational posterior for the latent space to be conditionally dependent on the value of the inducing points. We demonstrate that this more flexible variational posterior improves several metrics relating to the reconstruction of points on the data manifold.

发表机构

• LMU Munich（慕尼黑大学）
• Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
• Imperial College London（帝国理工学院）
• University of Technology Nuremberg (UTN)（纽伦堡工业大学）
• Helmholtz AI（亥姆霍兹人工智能中心）
• Xyme

机构由 AI 辅助整理，请以论文原文为准。