论文标题
多视级对称尖峰矩阵模型的信息理论限制
Information-theoretic limits of a multiview low-rank symmetric spiked matrix model
论文作者
论文摘要
我们考虑对重要类别的高维推理问题（即尖刺的对称矩阵模型）的概括，通常用作主要成分分析的概率模型。这种范式模型最近由于其现象学的丰富性和统计学到竞争性差距而引起了许多社区的关注，同时仍然可以进行处理。我们严格地通过单字母公式的证据来建立信息理论限制，以提供相互信息和最小均方误差。在技术方面，我们改善了最近引入的自适应插值方法，以便完全普遍地研究低级模型（即“高矩阵”的估计问题），这是对更复杂的推理和学习模型进行严格分析的重要一步。
We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis. Such paradigmatic models have recently attracted a lot of attention from a number of communities due to their phenomenological richness with statistical-to-computational gaps, while remaining tractable. We rigorously establish the information-theoretic limits through the proof of single-letter formulas for the mutual information and minimum mean-square error. On a technical side we improve the recently introduced adaptive interpolation method, so that it can be used to study low-rank models (i.e., estimation problems of "tall matrices") in full generality, an important step towards the rigorous analysis of more complicated inference and learning models.
