Controlled sequential Monte Carlo
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TL;DR: This method builds upon a number of existing algorithms in econometrics, physics, and statistics for inference in state space models, and generalizes these methods so as to accommodate complex static models.
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Abstract: Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in statistics and related fields; for example, for inference in nonlinear non-Gaussian state space models, and in complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which crucially impact their performance. We introduce here a class of controlled sequential Monte Carlo algorithms, where the proposal distributions are determined by approximating the solution to an associated optimal control problem using an iterative scheme. This method builds upon a number of existing algorithms in econometrics, physics and statistics for inference in state space models, and generalizes these methods so as to accommodate complex static models. We provide a theoretical analysis concerning the fluctuation and stability of this methodology that also provides insight into the properties of related algorithms. We demonstrate significant gains over state-of-the-art methods at a fixed computational complexity on a variety of applications.
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Citations
Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Nikolas Nüsken,Lorenz Richter,Lorenz Richter +2 more
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TL;DR: The potential of iterative diffusion optimisation techniques is investigated, in particular considering applications in importance sampling and rare event simulation, and focusing on problems without diffusion control, with linearly controlled drift and running costs that depend quadratically on the control.
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Credit Assignment Techniques in Stochastic Computation Graphs.
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Practical and Asymptotically Exact Conditional Sampling in Diffusion Models
TL;DR: The Twisted Diffusion Sampler (TDS) as mentioned in this paper is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models, which can provide exact samples for a broad range of conditional distributions without requiring task-specific training.
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Denoising Diffusion Samplers
Francisco Vargas,Will Grathwohl,Arnaud Doucet +2 more
- 27 Feb 2023
TL;DR: Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains as discussed by the authors , and they can be used to sample approximately from unnormalized probability density functions and estimate their normalizing constants.
•Posted Content
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Nikolas Nüsken,Lorenz Richter +1 more
TL;DR: In this paper, the authors investigated the potential of iterative diffusion optimisation techniques, in particular considering applications in importance sampling and rare event simulation, and developed a principled framework based on divergences between path measures.
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