Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for improving regression uncertainty estimation performance with a limited number of training data. The proposed method meta-learns how to calibrate uncertainty using data from various tasks by minimizing the test expected calibration error, and uses the knowledge for unseen tasks. We design our model such that the adaptation and calibration for each task can be performed without iterative procedures, which enables effective meta-learning. In particular, a task-specific uncalibrated output distribution is modeled by a GP with a task-shared encoder network, and it is transformed to a calibrated one using a cumulative density function of a task-specific Gaussian mixture model (GMM). By integrating the GP and GMM into our neural network-based model, we can meta-learn model parameters in an end-to-end fashion. Our experiments demonstrate that the proposed method improves uncertainty estimation performance while keeping high regression performance compared with the existing methods using real-world datasets in few-shot settings.

翻译：尽管深度核高斯过程（GP）在回归任务的元学习中已成功应用，但其不确定性估计性能可能较差。本文提出一种用于校准深度核高斯过程的元学习方法，以在训练数据有限的情况下提升回归不确定性估计性能。该方法通过最小化测试预期校准误差，利用多任务数据元学习不确定性校准方式，并将所学知识应用于未见任务。我们设计的模型使每个任务的适应与校准无需迭代过程即可完成，从而支持高效的元学习。具体而言，任务特定未校准输出分布由共享编码器网络的高斯过程建模，并通过任务特定高斯混合模型（GMM）的累积分布函数转化为校准分布。通过将高斯过程与GMM集成至基于神经网络的模型中，我们能够以端到端方式元学习模型参数。实验表明，在少样本场景下，相较于现有方法，所提方法在保持高回归性能的同时，显著提升了不确定性估计性能。