{"ID":2850215,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22157","arxiv_id":"2510.22157","title":"Stochastic Trace and Diagonal Estimator for Tensors","abstract":"We consider the problem of estimating the trace and diagonal entries of an N-order tensor (where $N \\geq 2$) under the framework where the tensor can only be accessed through tensor-vector multiplication. 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 and its extended version due to Bekas et al. 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 a tensor under this model. Our proposed methods can be seen as generalizations of Hutchinson's and Bekas et al.'s estimators and reduce to their estimators when N = 2. We provide a rigorous theoretical analysis of our proposals and complement it with supporting simulations.","short_abstract":"We consider the problem of estimating the trace and diagonal entries of an N-order tensor (where $N \\geq 2$) under the framework where the tensor can only be accessed through tensor-vector multiplication. The aim is to estimate the tensor's diagonal entries and trace by minimizing the number of tensor-vector queries. T...","url_abs":"https://arxiv.org/abs/2510.22157","url_pdf":"https://arxiv.org/pdf/2510.22157v1","authors":"[\"Bhisham Dev Verma\",\"Rameshwar Pratap\",\"Keegan Kang\"]","published":"2025-10-25T04:24:45Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.ST\"]","methods":"[]","has_code":false}