• Corpus ID: 53047267

A minimax near-optimal algorithm for adaptive rejection sampling

@article{Achdou2018AMN,
  title={A minimax near-optimal algorithm for adaptive rejection sampling},
  author={Juliette Achdou and Joseph C. Lam and Alexandra Carpentier and Gilles Blanchard},
  journal={ArXiv},
  year={2018},
  volume={abs/1810.09390}
}
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However, without proper tuning, this technique implies a high rejection rate. Several methods have been explored to cope with this problem, based on the principle of adaptively estimating the density by a simpler function, using the information of the previous samples. Most… 

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References

SHOWING 1-10 OF 32 REFERENCES

A generalization of the adaptive rejection sampling algorithm

This paper introduces a generalized adaptive rejection sampling procedure that can be applied with a broad class of target probability distributions, possibly non-log-concave and exhibiting multiple modes, and yields a sequence of proposal densities that converge toward the target pdf, thus achieving very high acceptance rates.

Adaptive rejection sampling with fixed number of nodes

This work proposes a novel ARS scheme, called Cheap Adaptive Rejection Sampling (CARS), where the computational effort for drawing from the proposal remains constant, decided in advance by the user.

Pliable Rejection Sampling

This paper presents pliable rejection sampling (PRS), a new approach to rejection sampling, where the sampling proposal is learned using a kernel estimator and the samples obtained are with high probability i.i.d. and distributed according to f.

Concave-Convex Adaptive Rejection Sampling

The applicability of the concave-convex approach on a number of standard distributions is demonstrated and an application to the efficient construction of sequential Monte Carlo proposal distributions for inference over genealogical trees is described.

Nonparametric Importance Sampling

It is shown that the nonparametric approach yields integral estimates that converge faster than estimates obtained from parametric approaches and that an adaptive method, which has been used successfully in parametric settings, does not yield better results than simple one-step methods in the non parametric setting.

Independent Doubly Adaptive Rejection Metropolis Sampling Within Gibbs Sampling

An alternative adaptive MCMC algorithm (IA2RMS) is proposed that overcomes an important drawback of the Adaptive Rejection Metropolis Sampling technique, speeding up the convergence of the chain to the target, allowing us to simplify the construction of the sequence of proposals, and thus reducing the computational cost of the entire algorithm.

Improved Adaptive Rejection Metropolis Sampling Algorithms

This work pinpointed a crucial drawback of the adaptive procedure used in ARMS: support points might never be added inside regions where the proposal is below the target, and the sequence of proposals never converges to the target.

Parsimonious Adaptive Rejection Sampling

This work proposes the Parsimonious Adaptive Rejection Sampling (PARS) method, where an efficient trade-off between acceptance rate and proposal complexity is obtained and the resulting algorithm is faster than the standard ARS approach.

A* Sampling

This work shows how sampling from a continuous distribution can be converted into an optimization problem over continuous space and presents a new construction of the Gumbel process and A* Sampling, a practical generic sampling algorithm that searches for the maximum of a Gumbels process using A* search.

The OS* Algorithm: a Joint Approach to Exact Optimization and Sampling

The OS* algorithm is a unied approach to exact optimization and sampling, based on incremental renements, that produces valid samples, but is unrealistically slow in high-dimension spaces.