This paper presents a Cramer-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy observations, (i.e., the tensor plus a random Gaussian i.i.d. tensor). A novel expression is derived for a bound on the mean square angular error of factors along a selected dimension of a tensor of an arbitrary dimension. The expression needs less operations for computing the bound, O(NR^6), than the best existing state-of-the art algorithm, O(N^3R^6) operations, where N and R are the tensor order and the tensor rank. Insightful expressions are derived for tensors of rank 1 and rank 2 of arbitrary dimension and for tensors of arbitrary dimension and rank, where two factor matrices have orthogonal columns.
The results can be used as a gauge of performance of different approximate CP decomposition algorithms, prediction of their accuracy, and for checking stability of a given decomposition of a tensor (condition whether the CRLB is finite or not). A novel expression is derived for a Hessian matrix needed in popular damped Gauss-Newton method for solving the CP decomposition of tensors with missing elements. Beside computing the CRLB for these tensors the expression may serve for design of damped Gauss-Newton algorithm for the decomposition.
Simula Metropolitan Center for Digital Engineering（西姆拉大都会数字工程中心）；Oslo Metropolitan Univ.（奥斯陆城市大学）；University of Rennes（雷恩大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；IRISA（法国雷恩信息系统与随机系统研究所）
PARAFAC2-based Coupled Matrix and Tensor Factorizations
Simula Metropolitan Center for Digital Engineering（西姆拉大都会数字工程中心）；Oslo Metropolitan University（奥斯陆城市大学）；Affiliated Zhongshan Hospital of Dalian University（大连大学附属中山医院）；Dalian University of Technology（大连理工大学）
针对现有 PARAFAC2 耦合矩阵-张量分解在正则化与耦合类型上的局限，本文提出结合 AO 与 ADMM 的算法框架，支持全模态约束和线性耦合，并通过实验验证其模式恢复准确性。
Unsupervised EHR-based Phenotyping via Matrix and Tensor Decompositions
Simula Metropolitan Center for Digital Engineering（西姆拉大都会数字工程中心）；Oslo Metropolitan University（奥斯陆城市大学）；Swammerdam Institute for Life Sciences, University of Amsterdam（阿姆斯特丹大学斯瓦默丹生命科学研究所）
FRAPPE: $\underline{\text{F}}$ast $\underline{\text{Ra}}$nk $\underline{\text{App}}$roximation with $\underline{\text{E}}$xplainable Features for Tensors
