mlsanityData to 7 Oct 2026

Feynman-Kac Operator Expectation Estimator

arXiv 2407.02010 ↗First posted 2 Jul 2024stat.ML cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

The Feynman-Kac Operator Expectation Estimator (FKEE) is an innovative method for estimating the target Mathematical Expectation mathbbEX~ P[f(X)] without relying on a large number of samples, in contrast to the commonly used Markov Chain Monte Carlo (MCMC) Expectation Estimator. FKEE comprises diffusion bridge models and approximation of the Feynman-Kac operator. The key idea is to use the solution to the Feynmann-Kac equation at the initial time u(x0,0)=mathbbE[f(XT)|X0=x0]. We use Physically Informed Neural Networks (PINN) to approximate the Feynman-Kac operator, which enables the incorporation of diffusion bridge models into the expectation estimator and significantly improves the efficiency of using data while substantially reducing the variance. Diffusion Bridge Model is a more general MCMC method. In order to incorporate extensive MCMC algorithms, we propose a new diffusion bridge model based on the Minimum Wasserstein distance. This diffusion bridge model is universal and reduces the training time of the PINN. FKEE also reduces the adverse impact of the curse of dimensionality and weakens the assumptions on the distribution of X and performance function f in the general MCMC expectation estimator. The theoretical properties of this universal diffusion bridge model are also shown. Finally, we demonstrate the advantages and potential applications of this method through various concrete experiments, including the challenging task of approximating the partition function in the random graph model such as the Ising model.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 32 of its 58 references that are in the map. First posted on arXiv 2 Jul 2024.

Builds on

32 of 58 references.

References · 32

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  3. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  4. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  5. 2021Variational Diffusion Modelscited by 1,145
  6. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  7. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 341
  8. 2013Black Box Variational Inferencecited by 317
  9. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  10. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  11. 2018Neural Importance Samplingcited by 154
  12. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
20 more
  1. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Modelscited by 102
  2. 2017Convergence of Langevin MCMC in KL-divergencecited by 86
  3. 2017Improved Variational Autoencoders for Text Modeling using Dilated Convolutionscited by 81
  4. 2019Discrete Flows: Invertible Generative Models of Discrete Datacited by 68
  5. 2021Efficient and Accurate Gradients for Neural SDEscited by 68
  6. 2014Control functionals for Monte Carlo integrationcited by 59
  7. 2018Banach Wasserstein GANcited by 56
  8. 2021Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEscited by 56
  9. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  10. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 37
  11. 2019High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithmcited by 36
  12. 2020Non-convex Learning via Replica Exchange Stochastic Gradient MCMCcited by 33
  13. 2013Langevin diffusions and the Metropolis-adjusted Langevin algorithmcited by 29
  14. 2022Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizationscited by 26
  15. 2020Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learningcited by 22
  16. 2015Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Familiescited by 15
  17. 2017Unbiased Markov chain Monte Carlo with couplingscited by 10
  18. 2020Semi-Exact Control Functionals From Sard's Methodcited by 9
  19. 2021Fast Doubly-Adaptive MCMC to Estimate the Gibbs Partition Function with Weak Mixing Time Boundscited by 3
  20. 2017Langevin diffusions on the torus: estimation and applicationscited by 2

Built on by

Not cited yet.