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Combining additivity and active subspaces for high-dimensional Gaussian process modeling

Mickael Binois, Victor Picheny

TL;DR

This contribution for high-dimensional Gaussian process modeling is to combine them with a multi-fidelity strategy, showcasing the advantages through experiments on synthetic functions and datasets.

Abstract

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the curse of dimensionality whenever the number of variables increases. This challenge is generally addressed by assuming additional structure in theproblem, the preferred options being either additivity or low intrinsic dimensionality. Our contribution for high-dimensional Gaussian process modeling is to combine them with a multi-fidelity strategy, showcasing the advantages through experiments on synthetic functions and datasets.

Combining additivity and active subspaces for high-dimensional Gaussian process modeling

TL;DR

This contribution for high-dimensional Gaussian process modeling is to combine them with a multi-fidelity strategy, showcasing the advantages through experiments on synthetic functions and datasets.

Abstract

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the curse of dimensionality whenever the number of variables increases. This challenge is generally addressed by assuming additional structure in theproblem, the preferred options being either additivity or low intrinsic dimensionality. Our contribution for high-dimensional Gaussian process modeling is to combine them with a multi-fidelity strategy, showcasing the advantages through experiments on synthetic functions and datasets.
Paper Structure (14 sections, 4 equations, 3 figures, 1 algorithm)

This paper contains 14 sections, 4 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Gaussian Processes Regression
  4. Additive Model
  5. Active Subspace Methods
  6. Multi-fidelity
  7. Multi-fidelity for High-dimensional Modeling
  8. Combination Options
  9. A Multi-fidelity Approach
  10. Proposed Instantiation
  11. Empirical Evaluation
  12. Setup
  13. Results
  14. Conclusion and Perspectives

Figures (3)

  • Figure 1: Additive model prediction surfaces on 20 points from the Branin function, interpolating (left) or approximating (right).
  • Figure 2: First part RMSE and score results. The color lines indicate the baseline result from standard GP models.
  • Figure 3: Second part RMSE and score results. The color lines indicate the baseline result from standard GP models.