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An Analysis of Vectorised Automatic Differentiation for Statistical Applications

Author

Listed:
  • Chun Fung Kwok

    (St. Vincent’s Institute of Medical Research, Melbourne 3065, Australia)

  • Dan Zhu

    (Department of Econometrics and Business Statistics, Monash University, Melbourne 3800, Australia)

  • Liana Jacobi

    (Department of Economics, University of Melbourne, Melbourne 3010, Australia)

Abstract

Automatic differentiation (AD) is a general method for computing exact derivatives in complex sensitivity analyses and optimisation tasks, particularly when closed-form solutions are unavailable and traditional analytical or numerical methods fall short. This paper introduces a vectorised formulation of AD grounded in matrix calculus. It aligns naturally with the matrix-oriented style prevalent in statistics, supports convenient implementations, and takes advantage of sparse matrix representation and other high-level optimisation techniques that are not available in the scalar counterpart. Our formulation is well-suited to high-dimensional statistical applications, where finite differences (FD) scale poorly due to the need to repeat computations for each input dimension, resulting in significant overhead, and is advantageous in simulation-intensive settings—such as Markov Chain Monte Carlo (MCMC)-based inference—where FD requires repeated sampling and multiple function evaluations, while AD can compute exact derivatives in a single pass, substantially reducing computational cost. Numerical studies are presented to demonstrate the efficacy and speed of the proposed AD method compared with FD schemes.

Suggested Citation

  • Chun Fung Kwok & Dan Zhu & Liana Jacobi, 2025. "An Analysis of Vectorised Automatic Differentiation for Statistical Applications," Stats, MDPI, vol. 8(2), pages 1-27, May.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:2:p:40-:d:1659287
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    References listed on IDEAS

    as
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