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New Tensor Train Vectors Enhance Matrix Trace Estimation

By PulseAugur Editorial · [2 sources] ·

Researchers have developed a new method for stochastic trace estimation using Gaussian random tensor train vectors. This approach offers a structured alternative to traditional methods, particularly for tensor-structured settings where unstructured vectors can be computationally expensive. The proposed technique, when applied with an appropriate tensor train rank, provides dimension-independent guarantees for the Girard--Hutchinson estimator and can achieve similar accuracy to classical methods. Furthermore, the study explores the integration of these sketches into the Nyström++ framework, potentially improving sample complexity under specific conditions. AI

IMPACT Introduces a more efficient method for matrix trace estimation in tensor-structured settings, potentially improving performance in ML algorithms.

RANK_REASON The cluster contains an academic paper detailing a new theoretical approach to a mathematical problem within machine learning.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New Tensor Train Vectors Enhance Matrix Trace Estimation

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Zvonimir Bujanovi\'c, Daniel Kressner, Hrvoje Oli\'c ·

    Stochastic trace estimation with tensor train random vectors

    arXiv:2606.15679v1 Announce Type: cross Abstract: Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products. However, in tensor-structured settings, unstructured Gaussian or Rademacher test vec…

  2. arXiv stat.ML TIER_1 English(EN) · Hrvoje Olić ·

    Stochastic trace estimation with tensor train random vectors

    Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products. However, in tensor-structured settings, unstructured Gaussian or Rademacher test vectors may be prohibitively expensive to store and c…

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