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Numerical Analysis Seminar
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Date, time & place | Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Norikazu Saito, Takahito Kashiwabara |
2024/03/13
16:30-17:30 Online
David Sommer (Weierstrass Institute for Applied Analysis and Stochastics)
Approximating Langevin Monte Carlo with ResNet-like neural network architectures (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
David Sommer (Weierstrass Institute for Applied Analysis and Stochastics)
Approximating Langevin Monte Carlo with ResNet-like neural network architectures (English)
[ Abstract ]
We analyse a method to sample from a given target distribution by constructing a neural network which maps samples from a simple reference distribution, e.g. the standard normal, to samples from the target distribution. For this, we propose using a neural network architecture inspired by the Langevin Monte Carlo (LMC) algorithm. Based on LMC perturbation results, approximation rates of the proposed architecture for smooth, log-concave target distributions measured in the Wasserstein-2 distance are shown. The analysis heavily relies on the notion of sub-Gaussianity of the intermediate measures of the perturbed LMC process. In particular, we derive bounds on the growth of the intermediate variance proxies under different assumptions on the perturbations. Moreover, we propose an architecture similar to deep residual neural networks (ResNets) and derive expressivity results for approximating the sample to target distribution map.
[ Reference URL ]We analyse a method to sample from a given target distribution by constructing a neural network which maps samples from a simple reference distribution, e.g. the standard normal, to samples from the target distribution. For this, we propose using a neural network architecture inspired by the Langevin Monte Carlo (LMC) algorithm. Based on LMC perturbation results, approximation rates of the proposed architecture for smooth, log-concave target distributions measured in the Wasserstein-2 distance are shown. The analysis heavily relies on the notion of sub-Gaussianity of the intermediate measures of the perturbed LMC process. In particular, we derive bounds on the growth of the intermediate variance proxies under different assumptions on the perturbations. Moreover, we propose an architecture similar to deep residual neural networks (ResNets) and derive expressivity results for approximating the sample to target distribution map.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
