48 lines
1.4 KiB
Markdown
48 lines
1.4 KiB
Markdown
---
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title: "固定均值高斯过程 (Fixed-Mean Gaussian Process)"
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created: 2026-06-17
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updated: 2026-06-17
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type: concept
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tags: [bayesian-deep-learning, uncertainty, gaussian-process, post-hoc]
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sources: [raw/papers/ortega-phd-thesis-2026.md]
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confidence: high
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---
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# 固定均值高斯过程 (Fixed-Mean Gaussian Process)
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FMGP 是 [[ortega-phd-thesis|Ortega (2026)]] 提出的**轻量级后处理不确定性校准方法**——在冻结的预训练网络上附加 GP 协方差结构。
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## 核心思想
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将预训练网络视为 GP 的**固定均值函数**：
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```
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f(x) ~ GP(μ_pretrained(x), k(x, x'))
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```
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- 均值 μ 由预训练网络提供（冻结，不再训练）
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- 协方差 k 由 GP 核参数化（可学习）
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## 优势
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- **极简**：仅需学习核参数，预训练网络完全不动
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- **校准**：GP 提供原则性的预测不确定性
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- **可扩展**：比完全 Bayesian 方法轻量得多
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- **兼容性**：可在任意预训练网络上附加
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## 与 VaLLA 的互补
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| 方法 | 校准来源 | 训练 |
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|------|---------|------|
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| [[variational-linearized-laplace-approximation|VaLLA]] | 权重后验 | 变分学习 Σ |
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| FMGP | GP 协方差 | 学习核参数 |
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两者提供互补的不确定性量化策略。
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## 参考
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- [[variational-linearized-laplace-approximation|VaLLA]]
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- [[bayesian-deep-learning|Bayesian 深度学习]]
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- [[gaussian-process|高斯过程]]
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- [[ortega-phd-thesis|论文]]
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