Pareto Smoothed Importance Sampling
By Aki Vehtari, Andrew Gelman, Jonah Gabry. Journal of machine learning research, 2015
295 citations recorded by the source corpus.
Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be noisy when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captured by the approximating distribution, in which case more stable estimates can be obtained by modifying extreme importance ratios. We present a new method for stabilizing importance weights using a generalized Pareto distribution fit to the upper tail of the distribution of the simulated importance ratios. The method, which empirically performs better than existing methods for stabilizing importance sampling estimates, includes stabilized effective sample size estimates, Monte Carlo error estimates and convergence diagnostics.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ae897d94109b00e0c143076f60d0f9013ccf5886
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In Statistics and Probability
- Yuling Yao
- Aki Vehtari
- Andrew Gelman
- Yong Luo
- Khaleel Al-Harbi
- Paul-Christian Burkner
- Jonah Gabry
- Daniel P. Simpson
Citations in the corpus
- Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors (2020, methodology): “We use Pareto smoothed importance sampling (PSIS, Vehtari et al., 2019b) to compute the defined LOO posterior (5).”
- Pathfinder: Parallel quasi-Newton variational inference (2021, unknown): “We adapt importance sampling using Pareto smoothed importance weights (Yao et al., 2018; Vehtari et al., 2019) to importance resampling to obtain more stable approximate draws.”
- Performances of LOO and WAIC as IRT Model Selection Methods (2017, background): “Interested readers are referred to Vehtari, Gelman, and Gabry (2015, 2016a).”