https://github.com/computorg/published-202402-elmasri-optimal

https://github.com/computorg/published-202402-elmasri-optimal

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• Host: GitHub
• URL: https://github.com/computorg/published-202402-elmasri-optimal
• Owner: computorg
• License: cc-by-4.0
• Created: 2024-02-12T10:57:45.000Z (over 2 years ago)
• Default Branch: master
• Last Pushed: 2025-06-03T09:26:51.000Z (about 1 year ago)
• Last Synced: 2025-06-03T20:28:34.016Z (about 1 year ago)
• Language: TeX
• Homepage: http://computo.sfds.asso.fr/published-202402-elmasri-optimal/
• Size: 3.29 MB
• Stars: 1
• Watchers: 4
• Forks: 0
• Open Issues: 4
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# Optimal projection for parametric importance sampling in high dimensions

Maxime El Masri, Jérôme Morio, Florian Simatos

2024-03-11

### Citation

Maxime El Masri, Jérôme Morio and Florian Simatos (March 2024). Optimal projection for parametric importance sampling in high dimensions. Computo.

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### Authors’ affiliations

- Maxime El Masri (ONERA/DTIS, ISAE-SUPAERO, Université de Toulouse)

- [Jérôme Morio](https://www.onera.fr/en/staff/jerome-morio?destination=node/981) (ONERA/DTIS, Université de Toulouse)

- [Florian Simatos](https://pagespro.isae-supaero.fr/florian-simatos/) (ISAE-SUPAERO, Université de Toulouse)

### Abstract

We propose a dimension reduction strategy in order to improve the

performance of importance sampling in high dimensions. The idea is to

estimate variance terms in a small number of suitably chosen directions.

We first prove that the optimal directions, i.e., the ones that minimize

the Kullback–Leibler divergence with the optimal auxiliary density, are

the eigenvectors associated with extreme (small or large) eigenvalues of

the optimal covariance matrix. We then perform extensive numerical

experiments showing that as dimension increases, these directions give

estimations which are very close to optimal. Moreover, we demonstrate

that the estimation remains accurate even when a simple empirical

estimator of the covariance matrix is used to compute these directions.

The theoretical and numerical results open the way for different

generalizations, in particular the incorporation of such ideas in

adaptive importance sampling schemes.