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traceax: a JAX-based framework for stochastic trace estimation.

Abdullah Al Nahid1, Linda Serafin2, Nicholas Mancuso3,2,4

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Stochastic trace estimation provides a memory-efficient solution for large matrices in machine learning and statistics. The new traceax framework enables scalable, accurate trace estimation with Python, reducing computational costs.

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Area of Science:

  • Computational mathematics
  • Machine learning
  • Statistical inference

Background:

  • Matrix trace calculation is essential but often memory-prohibitive.
  • Stochastic trace estimation offers a viable alternative using randomized methods.
  • Existing methods may lack scalability or integration capabilities.

Purpose of the Study:

  • Introduce traceax, a Python framework for scalable stochastic trace estimation.
  • Demonstrate traceax's efficiency and accuracy compared to direct computation.
  • Facilitate integration of advanced trace estimators into inferential pipelines.

Main Methods:

  • Leveraging linear operator representations for efficient matrix handling.
  • Implementing state-of-the-art stochastic trace estimators.
  • Utilizing automatic differentiation and hardware acceleration for performance.

Main Results:

  • Simulations confirm high accuracy of traceax estimators.
  • Significant reductions in runtime and memory usage demonstrated.
  • Successful implementation of a stochastic heritability estimator as a proof of concept.

Conclusions:

  • traceax offers a versatile and scalable tool for stochastic trace estimation.
  • The framework supports efficient integration into existing machine learning and statistical pipelines.
  • Enables advanced trace estimation for large-scale problems.