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Detection Is Harder Than Estimation in Certain Regimes: Inference for Moment and Cumulant Tensors
Runshi Tang, Yuefeng Han, Anru R. Zhang
We study estimation and detection of high-order moment and cumulant tensors from i.i.d.\ observations of a -dimensional random vector, with performance measured in tensor sp…
From Reverse Detection--Estimation Gaps to Computational Lower Bounds for Norm Approximation
Runshi Tang, Yuefeng Han, Anru R. Zhang
We develop a general reduction scheme that converts reverse detection--estimation gaps into computational lower bounds for norm approximation. If an efficiently computable estimato…
Statistical Inference for Low-Rank Tensors: Heteroskedasticity, Subgaussianity, and Applications
Joshua Agterberg, Anru Zhang
In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the hi…
Estimating Higher-Order Mixed Memberships via the Tensor Perturbation Bound
Joshua Agterberg, Anru Zhang
Higher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures, where each component (node) along each different mode has…