低秩偶数阶对称张量估计的互信息
Mutual information for low-rank even-order symmetric tensor estimation
摘要：
考虑有限秩对称张量分解的统计模型，证明了当张量为偶数阶时，其渐近互信息的单字母变分表达式。证明应用自适应插值方法最初发明的秩一分解。在这里，我们展示了如何将自适应插值扩展到有限秩和偶数阶张量。这就需要新的非平凡的想法，在目前的分析文献。我们还强调证明不足时，处理奇数阶张量。
英文摘要：
We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new nontrivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.
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。
