Academic Journal
DEEP IMPORTANCE SAMPLING USING TENSOR TRAINS WITH APPLICATION TO A PRIORI AND A POSTERIORI RARE EVENTS
| العنوان: | DEEP IMPORTANCE SAMPLING USING TENSOR TRAINS WITH APPLICATION TO A PRIORI AND A POSTERIORI RARE EVENTS |
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| المؤلفون: | Cui, Tiangang, Dolgov, Sergey, Scheichl, Robert |
| المصدر: | Cui , T , Dolgov , S & Scheichl , R 2024 , ' DEEP IMPORTANCE SAMPLING USING TENSOR TRAINS WITH APPLICATION TO A PRIORI AND A POSTERIORI RARE EVENTS ' , SIAM Journal on Scientific Computing , vol. 46 , no. 1 , pp. C1-C29 . https://doi.org/10.1137/23M1546981 |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | Bayesian inference, inverse problems, rare events, tensor train, transport maps, /dk/atira/pure/subjectarea/asjc/2600/2605, name=Computational Mathematics, /dk/atira/pure/subjectarea/asjc/2600/2604, name=Applied Mathematics |
| الوصف: | We propose a deep importance sampling method that is suitable for estimating rare event probabilities in high-dimensional problems. We approximate the optimal importance distribution in a general importance sampling problem as the pushforward of a reference distribution under a composition of order-preserving transformations, in which each transformation is formed by a squared tensor-train decomposition. The squared tensor-train decomposition provides a scalable ansatz for building order-preserving high-dimensional transformations via density approximations. The use of a composition of maps moving along a sequence of bridging densities alleviates the difficulty of directly approximating concentrated density functions. To compute expectations over unnormalized probability distributions, we design a ratio estimator that estimates the normalizing constant using a separate importance distribution, again constructed via a composition of transformations in tensor-train format. This offers better theoretical variance reduction compared to self-normalized importance sampling and thus opens the door to efficient computation of rare event probabilities in Bayesian inference problems. Numerical experiments on problems constrained by differential equations show little to no increase in the computational complexity of the estimator when the event probability goes to zero, enabling us to compute hitherto unattainable estimates of rare event probabilities for complex, high-dimensional posterior densities. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| DOI: | 10.1137/23M1546981 |
| الاتاحة: | https://researchportal.bath.ac.uk/en/publications/bf49cd02-ffe3-4e13-94f9-1be79f0677d6 https://doi.org/10.1137/23M1546981 https://purehost.bath.ac.uk/ws/files/315295671/23m1546981.pdf http://www.scopus.com/inward/record.url?scp=85184037883&partnerID=8YFLogxK https://arxiv.org/pdf/2209.01941.pdf |
| Rights: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.277DBB14 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1137/23M1546981 |
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