Meta-learning is a framework in which machine learning models train over a set of datasets in order to produce predictions on new datasets at test time. Probabilistic meta-learning has received an abundance of attention from the research community in recent years, but a problem shared by many existing probabilistic meta-models is that they require a very large number of datasets in order to produce high-quality predictions with well-calibrated uncertainty estimates. In many applications, however, such quantities of data are simply not available. In this dissertation we present a significantly more data-efficient approach to probabilistic meta-learning through per-datapoint amortisation of inference in Bayesian neural networks, introducing the Amortised Pseudo-Observation Variational Inference Bayesian Neural Network (APOVI-BNN). First, we show that the approximate posteriors obtained under our amortised scheme are of similar or better quality to those obtained through traditional variational inference, despite the fact that the amortised inference is performed in a single forward pass. We then discuss how the APOVI-BNN may be viewed as a new member of the neural process family, motivating the use of neural process training objectives for potentially better predictive performance on complex problems as a result. Finally, we assess the predictive performance of the APOVI-BNN against other probabilistic meta-models in both a one-dimensional regression problem and in a significantly more complex image completion setting. In both cases, when the amount of training data is limited, our model is the best in its class.

翻译：元学习是一种机器学习框架，模型在一组数据集上训练，以便在测试时对新数据集进行预测。近年来，概率元学习受到了研究界的广泛关注，但许多现有概率元模型存在一个共同问题：它们需要非常大量的数据集才能产生具有良好校准不确定度估计的高质量预测。然而，在许多实际应用中，这种数量的数据根本不可用。在本论文中，我们提出了一种显著更数据高效的概率元学习方法，通过逐数据点摊销贝叶斯神经网络中的推断，引入了摊销伪观测变分推断贝叶斯神经网络（APOVI-BNN）。首先，我们表明，尽管摊销推断仅通过单次前向传播完成，但在我们提出的摊销方案下获得的近似后验质量与传统变分推断相当或更优。接着，我们讨论了APOVI-BNN如何被视为神经过程家族的新成员，从而激励使用神经过程训练目标，以潜在提升复杂问题上的预测性能。最后，我们在一个一维回归问题和一个复杂度显著更高的图像补全场景中，评估了APOVI-BNN与其他概率元模型的预测性能。在这两种情况下，当训练数据量有限时，我们的模型在其同类中表现最佳。