scholarly journals Gaussian Process Based Expected Information Gain Computation for Bayesian Optimal Design

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 258
Author(s):  
Zhihang Xu ◽  
Qifeng Liao
Keyword(s):  
Monte Carlo ◽  
Optimal Design ◽  
Information Gain ◽  
Computational Cost ◽  
Bayesian Optimization ◽  
Likelihood Functions ◽  
Expected Information ◽  
Bayesian Optimal Design ◽  
Bayesian Monte Carlo ◽  
Expected Information Gain

Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to efficiently compute the EIG, and a Bayesian optimization (BO) strategy is proposed to obtain its maximizer only using a small number of samples. For Bayesian Monte Carlo posed on uniform and normal distributions, our analysis provides explicit expressions for the mean estimates and the bounds of their variances. The accuracy and the efficiency of our DLBMC and BO based optimal design are validated and demonstrated with numerical experiments.

Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Piyush Pandita ◽  
Ilias Bilionis ◽  
Jitesh Panchal
Keyword(s):  
Optimal Design ◽  
Design Of Experiments ◽  
Information Gain ◽  
Black Box ◽  
Expected Information ◽  
Bayesian Optimal Design ◽  
Physical Response ◽  
Hypothetical Experiment ◽  
Statistical Expectation ◽  
Expected Information Gain

Abstract Bayesian optimal design of experiments (BODEs) have been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty propagation and design under uncertainty problems. Our hypothesis is that an optimal BODE should be maximizing the expected information gain in the QoI. We represent the information gain from a hypothetical experiment as the Kullback–Liebler (KL) divergence between the prior and the posterior probability distributions of the QoI. The prior distribution of the QoI is conditioned on the observed data, and the posterior distribution of the QoI is conditioned on the observed data and a hypothetical experiment. The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response. The developed BODE is validated on synthetic functions with varying number of input-dimensions. We demonstrate the performance of the methodology on a steel wire manufacturing problem.

scholarly journals Visual attention maximizes expected information gain in goal inference

2021 ◽  
Vol 21 (9) ◽  
pp. 2187
Author(s):  
Bohao Shi ◽  
Zhen Li ◽  
Yazhen Peng ◽  
Zhuoxuan Liu ◽  
Jifan Zhou ◽  
...  
Keyword(s):  
Visual Attention ◽  
Information Gain ◽  
Expected Information ◽  
Expected Information Gain ◽  
Goal Inference

Bayesian optimal design of fixed knockout tournament brackets

2016 ◽  
Vol 12 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Jonathan Hennessy ◽  
Mark Glickman
Keyword(s):  
Monte Carlo ◽  
Simulated Annealing ◽  
Optimal Design ◽  
Expected Utility ◽  
Partial Information ◽  
Direct Computation ◽  
Monte Carlo Estimate ◽  
Bayesian Optimal Design ◽  
Knockout Tournament ◽  
Carlo Estimate

AbstractWe present a methodology for finding globally optimal knockout tournament designs when partial information is known about the strengths of the players. Our approach involves maximizing an expected utility through a Bayesian optimal design framework. Given the prohibitive computational barriers connected with direct computation, we compute a Monte Carlo estimate of the expected utility for a fixed tournament bracket, and optimize the expected utility through simulated annealing. We demonstrate our method by optimizing the probability that the best player wins the tournament. We compare our approach to other knockout tournament designs, including brackets following the standard seeding. We also demonstrate how our approach can be applied to a variety of other utility functions, including whether the best two players meet in the final, the consistency between the number of wins and the player strengths, and whether the players are matched up according to the standard seeding.

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