Adaptive Stratified Sampling for Monte-Carlo integration of Differentiable functions
@inproceedings{Carpentier2012AdaptiveSS, title={Adaptive Stratified Sampling for Monte-Carlo integration of Differentiable functions}, author={Alexandra Carpentier and R{\'e}mi Munos}, booktitle={NIPS}, year={2012} }
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are well spread on the domain (this notion shares similitude with low discrepancy). We prove that the estimate returned by the algorithm is almost similarly accurate as the estimate that…
8 Citations
Toward Optimal Stratification for Stratified Monte-Carlo Integration
- Computer ScienceICML
- 2013
An algorithm is provided that selects online, among a large class of partitions, the partition that provides the optimal trade-off, and allocates the samples almost optimally on this partition.
Approximate Function Evaluation via Multi-Armed Bandits
- Computer Science, MathematicsAISTATS
- 2022
This work designs an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least 1 − δ returns an ε accurate estimate of f ( µ ).
Adaptive Monte Carlo via Bandit Allocation
- Mathematics, EconomicsICML
- 2014
It is shown that well developed allocation strategies can be used to achieve an MSE that approaches that of the best estimator chosen in retrospect, and a new set of adaptive Monte Carlo strategies are developed that provide stronger guarantees than previous approaches while offering practical advantages.
Sampling-Based Uncertainty Quantification: Monte Carlo and Beyond
- Mathematics
- 2018
This chapter covers sampling methods beginning with Monte Carlo sampling and before proceeding to more sophisticated sampling procedures. In Sect. 7.1 the basic Monte Carlo methods are detailed and…
Learning Multiple Markov Chains via Adaptive Allocation
- Computer Science, MathematicsNeurIPS
- 2019
A novel learning algorithm is presented that efficiently balances exploration and exploitation intrinsic to this problem, without any prior knowledge of the chains, and it is shown that the algorithm asymptotically attains an optimal loss.
M ay 2 01 9 Learning Multiple Markov Chains via Adaptive Allocation
- Computer Science, Mathematics
- 2019
A novel learning algorithm is presented that efficiently balances exploration and exploitation intrinsic to this problem, without any prior knowledge of the chains, and it is shown that the algorithm asymptotically attains an optimal loss.
Reliability analysis of shell truss structure by hybrid Monte Carlo method
- Engineering
- 2020
The paper presents an example of reliability analysis of shell structures susceptible to stability loss from the condition of node snapping, which assumes the use of Neural Networks in Monte Carlo (MC) simulations to analyze the reliability of the structure.
References
SHOWING 1-10 OF 10 REFERENCES
Adaptive Optimal Allocation in Stratified Sampling Methods
- Mathematics
- 2007
In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of…
Empirical Bernstein Bounds and Sample-Variance Penalization
- Mathematics, Computer ScienceCOLT
- 2009
Improved constants for data dependent and variance sensitive confidence bounds are given, called empirical Bernstein bounds, and extended to hold uniformly over classes of functions whose growth function is polynomial in the sample size n, and sample variance penalization is considered.
Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
- Computer Science
- 1981
The authoritative resource for understanding the power behind Monte Carlo Methods and a new co-author has been added to enliven the writing style and to provide modern day expertise on new topics.
Simulation and the Monte Carlo method
- PhysicsWiley series in probability and mathematical statistics
- 1981
From the Publisher:
Provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide…
Exploration-exploitation tradeoff using variance estimates in multi-armed bandits
- Computer ScienceTheor. Comput. Sci.
- 2009
Monte Carlo Methods in Financial Engineering
- Computer Science
- 2003
This paper presents a meta-modelling procedure that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually computing random numbers and random Variables.
Adaptive Stratified Sampling for Monte-Carlo integration of Differentiable functions
- Technical report,
- 2012
Finite Time Analysis of Stratified Sampling for Monte Carlo
- Mathematics, Computer ScienceNIPS
- 2011
This work proposes a strategy that samples the arms according to an upper bound on their standard deviations and compares its estimation quality to an ideal allocation that would know the standard deviations of the strata.
Active learning and its application to heteroscedastic problems
- Department of Computing Science, Univ. of Alberta, MSc thesis,
- 2009