用潜在因子建模高维输出，小样本下仍能精准预测气候模拟结果。
Gaussian Process Latent Factor Regression for Low-Data, High-Dimensional Output Problems
- 将输出分解为低维潜在变量的线性组合，通过高斯过程建模潜在状态变化。
- 在仅100个训练样本下，对超过10万维的气候数据实现高精度预测。
- 适合小样本、高维输出的科学模拟任务，如外星行星气候建模。
在科学领域，回归任务常需从少量训练样本预测高维输出。多输出高斯过程虽在小样本下表现优异，但难以处理高维输出。压缩-预测流水线（如PCA-GP）虽能应对高维，却依赖重建最优的基底，而非预测性能。为此，我们提出一种新模型：将每个输出表示为从高斯过程先验中采样的低维潜在状态的线性-高斯解码结果。通过解析边缘化解码权重，将压缩与预测统一于单一目标函数，实现对高维输出的高效建模。该模型称为高斯过程潜在因子回归（GPLFR）。我们在岩石系外行星全球气候模型上构建了首个空间分辨的模拟器，验证了其有效性。
原文摘要 · Abstract (English)
In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples. Multi-output Gaussian processes excel in low-data regimes but typically struggle with high-dimensional outputs. Compress-then-predict pipelines such as PCA-GP (principal component analysis plus Gaussian process regression) handle high dimensionality, but rely on bases optimized for reconstruction rather than prediction. To address this gap, we propose a model that represents each output as a linear-Gaussian decoding of a low-dimensional latent state drawn from a Gaussian process prior. By analytically marginalizing the decoder weights, we couple compression and prediction in a single objective that scales to high-dimensional outputs. We refer to this model as Gaussian process latent factor regression (GPLFR). We demonstrate GPLFR by building the first spatially resolved emulator of global climate models for rocky exoplanets.
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