Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samples
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify its statistics, using the minimum number of function evaluations. This problem can been seen in the context of active learning or optimal experimental design. We employ Bayesian regression to represent the derived model uncertainty due to finite and small number of input-output pairs. In this context we evaluate existing methods for optimal sample selection, such as model error minimization and mutual information maximization. We show that for the case of known output variance, the commonly employed criteria in the literature do not take into account the output values of the existing input-output pairs, while for the case of unknown output variance this dependence can be very weak. We introduce a criterion that takes into account the values of the output for the existing samples and adaptively selects inputs from regions of the parameter space which have important contribution to the output. The new method allows for application to high-dimensional inputs, paving the way for optimal experimental design in high-dimensions.
Code (0)
등록된 구현이 없습니다.
Tasks
Active LearningExperimental DesignregressionSimilar Papers 제목 키워드 기반
Bayesian Optimization with Output-Weighted Optimal Sampling
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbers…
Bayesian OptimizationClosed-Loop phase selection in EEG-TMS using Bayesian Optimization
Research on transcranial magnetic stimulation (TMS) combined with encephalography feedback (EEG-TMS) has shown that the phase of the sensorimotor mu rhythm is predictive of corticospinal excitability. Thus, if the subjec…
Bayesian OptimizationEEGregressionRhythmOptimal Subsampling Approaches for Large Sample Linear Regression
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes …
regressionEfficient Exploration through Bayesian Deep Q-Networks
We study reinforcement learning (RL) in high dimensional episodic Markov decision processes (MDP). We consider value-based RL when the optimal Q-value is a linear function of d-dimensional state-action feature representa…
Atari GamesEfficient ExplorationregressionReinforcement Learning+2Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification
We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradig…
Active LearningExperimental DesignUncertainty Quantification