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Monte Carlo Sampling Methods
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The integral over x, z and y can be approximated by Monte Carlo sampling, simplifying J_E-MIB.
“Finally, the integral over x , z and y can be approximated by Monte Carlo sampling [49], and thus J E -MIB (Eq. 8) can be simplified as:”
From Multimodal Information Bottleneck: Learning Minimal Sufficient Unimodal and Multimodal Representations (2023) · cites this paper as [49]
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Research works printed but not linked: 32
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“For each cell population (e.g., cell type), we approximate its distribution using a Monte Carlo Sampling strategy 120 involving the sampling of each dimension of the latent embeddings a thousand times to form a multivariate normal distribution.”
Method
Metadata
- Authors
- Shapiro, A.
- Affiliations
- Georgia Institute of Technology (US)
- Corresponding author
- Shapiro, Alexander
- ORCID
- Shapiro, Alexander
- Venue
- Handbooks in Operations Research and Management Science
- Publisher
- Elsevier
- Published
- 2003
- Pages
- 353-425
- ISSN
- 0927-0507 (ISSN-L)
- OpenAlex
- W1490324987
- Cited by
- 916
- References
- 0
- Citations by year
- 2026: 31 · 2025: 55 · 2024: 53 · 2023: 38 · 2022: 42 · 2021: 61 · 2020: 45 · 2019: 46 · 2018: 36 · 2017: 28 · 2016: 32 · 2015: 43 · 2014: 31 · 2013: 46 · 2012: 50
- FWCI
- 78.42
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Handbooks in operations research and management science (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Risk and Portfolio Optimization
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- sample average approximation, stochastic programming, large-scale optimization, estimator properties, error estimation, variance reduction, multistage stochastic programming, variational inequalities
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