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Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samples.

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This study introduces a new Bayesian regression criterion for optimal experimental design. It adaptively selects inputs to efficiently identify unknown function statistics, improving high-dimensional problem-solving.

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Area of Science:

  • Computational statistics
  • Machine learning
  • Applied mathematics

Background:

  • Identifying unknown function statistics from limited data is crucial for many problems.
  • This challenge is common in active learning and optimal experimental design.
  • Bayesian regression is used to model uncertainty from sparse input-output data.

Purpose of the Study:

  • To evaluate existing methods for optimal sample selection in Bayesian regression.
  • To develop a new criterion for adaptive input selection in high-dimensional parameter spaces.
  • To improve the efficiency of identifying unknown function statistics with minimal evaluations.

Main Methods:

  • Bayesian regression to quantify model uncertainty.
  • Evaluation of existing optimal sample selection criteria (model error minimization, mutual information maximization).
  • Introduction and application of a novel criterion considering output values of existing samples.

Main Results:

  • Existing criteria often neglect output values, especially with unknown output variance.
  • The new criterion adaptively selects inputs based on their contribution to the output.
  • The proposed method is applicable to high-dimensional input spaces.

Conclusions:

  • A new, adaptive criterion enhances optimal experimental design by utilizing existing data effectively.
  • This approach addresses limitations of current methods in identifying unknown function statistics.
  • The method facilitates optimal experimental design in complex, high-dimensional scenarios.