Convergence of adaptive mixtures of importance sampling schemes
By Randal Douc, Arnaud Guillin, Jean-Michel Marin, Christian P. Robert. 2007
132 citations recorded by the source corpus.
In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given simulation kernel can clarify a posteriori how adequate this kernel is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for adaptive mixtures of population Monte Carlo algorithms and show that Rao--Blackwellized versions asymptotically achieve an optimum in terms of a Kullback divergence criterion, while more rudimentary versions do not benefit from repeated updating.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Ingmar Schuster
- Christian P. Robert
- Jean-Michel Marin
- Eric Moulines
- Jean-Marie Cornuet
- Olivier Capp'e
- Antonietta Mira
- Arnaud Guillin
In Statistics and Probability
- Christian P. Robert
- Ingmar Schuster
- Jean-Michel Marin
- Antonietta Mira
- Arnaud Guillin
- Jean-Marie Cornuet
- Eric Moulines
- Randal Douc
Citations in the corpus
- Gradient Importance Sampling (2015, methodology): “After collecting new samples, D-Kernel approximations [16] or Mixture distributions (such as Mixtures of Gaus-sians or Student-T mixtures) [17] are updated to fit the posterior better.”
- An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo (2007, background): “αm are the parameters of the proposal to be adapted are given in [112], [113].”
- Approximate Bayesian computational methods (2011, methodology): “An alternative version called ABC-PMC and based on genuine importance sampling arguments, proposed by Beaumont et al. (2009), bypasses this difficulty, in connection with the population Monte Carlo method of Douc et al. (2007).”
- Adaptive Multiple Importance Sampling (2009, background): “These two different strategies give essentially the same results.”
- Minimum variance importance sampling via Population Monte Carlo (2007, background): “It is garanteed in cases like those of Douc et al. (2006) updating scheme and we will show below that it also holds for our updating scheme.”