Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization
Updated 5 h ago · first seen 11 Sept 2026
paper_01M294FT7KZY99CNS5VSVCCDSB
- Published
- 11 Sept 2026
- T1 · 5 h ago
- arXiv
- 2605.20145
- T1 · 5 h ago
- Category
- stat.ML
- T1 · 5 h ago
Abstract
-cross Abstract: Gaussian process (GP) predictive distributions are commonly used in Bayesian optimization (BO) to guide the selection of evaluation points for expensive objective functions. The choice of kernel and hyperparameters has a strong influence on the exploration--exploitation trade-off. For minimization, sampling criteria such as expected improvement (EI) depend on both the probability mass below the current best value and the shape of the predictive distribution in this region. This article studies goal-oriented calibration of GP predictive distributions below a low threshold $t$ in the noiseless setting, for standard GP models with hyperparameters selected by maximum likelihood. We consider two complementary forms of calibration below $t$ for inputs distributed according to a reference measure $\mu$: occurrence calibration over the design space and thresholded $\mu$-calibration on sublevel sets of the form $\{x\in\mathbb{X}, f(x)\le t\}$. We propose tcGP, a post-hoc method that combines these two forms of calibration for GP predictive distributions below $t$. With fixed GP hyperparameters, the exact EI sampling criterion based on tcGP generates a sequence of evaluation points that is dense in the design space. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and globally calibrated GP models.
Authors 2
Aur\'elien Pion, Emmanuel Vazquez
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Arxiv announce type
- replace
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- arXiv id
- 2605.20145
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Categories
- stat.ML, cs.LG, stat.ME
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Primary category
- stat.ML
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
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Attributed facts
9
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T19
Freshest observation
5 h ago
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- Authors
- Aur\'elien Pion, Emmanuel Vazquez
As of
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Claim history
Official pageofficial_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/abs/2605.20145 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| -cross Abstract: Gaussian process (GP) predictive distributions are commonly used in Bayesian optimization (BO) to guide the selection of evaluation points for expensive objective functions. The choice of kernel and hyperparameters has a strong influence on the exploration--exploitation trade-off. For minimization, sampling criteria such as expected improvement (EI) depend on both the probability mass below the current best value and the shape of the predictive distribution in this region. This article studies goal-oriented calibration of GP predictive distributions below a low threshold $t$ in the noiseless setting, for standard GP models with hyperparameters selected by maximum likelihood. We consider two complementary forms of calibration below $t$ for inputs distributed according to a reference measure $\mu$: occurrence calibration over the design space and thresholded $\mu$-calibration on sublevel sets of the form $\{x\in\mathbb{X}, f(x)\le t\}$. We propose tcGP, a post-hoc method that combines these two forms of calibration for GP predictive distributions below $t$. With fixed GP hyperparameters, the exact EI sampling criterion based on tcGP generates a sequence of evaluation points that is dense in the design space. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and globally calibrated GP models. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Arxiv announce typearxiv_announce_type1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| replace | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
arXiv idarxiv_id1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 2605.20145 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Categoriescategories1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| stat.ML, cs.LG, stat.ME | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
PDFpdf_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/pdf/2605.20145 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Primary categoryprimary_category1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| stat.ML | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Publishedpublished_at1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 11 Sept 2026 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →
New paper: Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 3 h ago | 1 |
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