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Accelerating Particle-based Energetic Variational Inference

arXiv 2504.03158 ↗First posted 4 Apr 2025stat.ML cs.LGcited by 0

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Abstract (arXiv)

In this work, we propose a new particle-based variational inference (ParVI) method for accelerating the Energetic Variational Inference with Implicit scheme (EVI-Im) introduced in Ref. citewang2021particle. Inspired by energy quadratization (EQ) and operator splitting techniques for gradient flows, the proposed method efficiently drives particles towards the target distribution, while retaining a meaningful stability mechanism. Unlike EVI-Im, which employs the implicit Euler method to solve variational-preserving particle dynamics obtained from a "discretization-then-variation" approach for minimizing the Kullback--Leibler divergence, the proposed algorithm avoids repeated evaluation of inter-particle interaction terms within each time step, significantly reducing computational cost. The framework is also extensible to other gradient-based sampling techniques. Through several numerical experiments, we demonstrate that the proposed method achieves competitive performance compared with existing ParVI approaches, while offering advantages in efficiency and robustness in certain regimes.

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References · 23

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11 more
  1. 2019Stein Variational Gradient Descent With Matrix-Valued Kernelscited by 32
  2. 2017Riemannian Stein Variational Gradient Descent for Bayesian Inferencecited by 24
  3. 2019A consensus-based global optimization method for high dimensional machine learning problemscited by 23
  4. 2019Projected Stein Variational Newton: A Fast and Scalable Bayesian Inference Method in High Dimensionscited by 21
  5. 2020Particle-based Energetic Variational Inferencecited by 14
  6. 2023Energy-Dissipative Evolutionary Deep Operator Neural Networkscited by 14
  7. 2020AEGD: Adaptive Gradient Descent with Energycited by 6
  8. 2021A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernelcited by 3
  9. 2022An Adaptive Gradient Method with Energy and Momentumcited by 3
  10. 2022Dynamic behavior for a gradient algorithm with energy and momentumcited by 2
  11. 2023Adaptive Preconditioned Gradient Descent with Energycited by 1

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