Stochastic Trace and Diagonal Estimator for Tensors

Publication Date

Fall 2026

Description

We consider the problem of estimating the trace and diagonal entries of an $N$-order tensor (where $N \geq 2$) under a tensor-vector framework, in which the tensor can only be accessed through tensor-vector multiplications. The aim is to estimate the tensor’s diagonal entries and trace by minimizing the number of tensor-vector queries. The seminal work of Hutchinson [1], and [2] give unbiased estimates of the trace and diagonal elements of a given matrix, respectively, using matrix-vector queries. However, to the best of our knowledge, no analogous results are known for estimating the trace and diagonal entries of higher-order tensors using tensor-vector queries. This paper addresses this gap and presents unbiased estimators for the trace and diagonal entries of tensors under this model. Our proposed methods can be seen as generalizations of [1, 2], and reduce to their estimators for the matrix when $N=2$. We provide a rigorous theoretical analysis of our proposals and complement it with supporting simulations.

Journal

Theoretical Computer Science

Volume

1083

Department

Mathematics

DOI

https://doi.org/10.1016/j.tcs.2026.116154

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