Gaussian process state-space models (GPSSMs) provide a principled and
flexible approach to model latent state dynamics observed through emission
models. However, existing variational methods for learning GPSSMs face a
substantial challenge in optimizing a large number of parameters, particularly
with the introduction of amortized inference networks. To address this
challenge, we leverage the ensemble Kalman filter (EnKF), a well-established
model-based filtering technique, to approximate the posterior distribution of
latent states within the variational inference framework. This approach
eliminates the need for inference networks, significantly reducing the number
of variational parameters. Moreover, we demonstrate that with the aid of EnKF,
the straightforward evaluation of approximated evidence lower bound (ELBO) in
the variational inference can be easily obtained through the summation of
multiple terms with closed-form solutions. By leveraging automatic
differentiation tools, we thus can maximize the ELBO and train the GPSSM
efficiently. We also extend the proposed method to an online setting and
provide comprehensive algorithm analyses and insights. Extensive testing on
diverse real and simulated datasets demonstrates that our variational inference
algorithms, integrated with EnKF, outperform existing methods in terms of
learning and inference performance.

通过集成卡尔曼滤波器（EnKF）近似推断隐藏状态的后验分布，我们提出了一种改进的变分推断方法，有效地训练高斯过程状态空间模型（GPSSM），并在学习和推断性能方面优于现有方法。

集合卡尔曼滤波辅助变分推断在高斯过程态空间模型中的应用

Ensemble Kalman Filtering-Aided Variational Inference for Gaussian  Process State-Space Models

Meta-learning for few-shot learning allows a machine to leverage previously
acquired knowledge as a prior, thus improving the performance on novel tasks
with only small amounts of data. However, most mainstream models suffer from
catastrophic forgetting and insufficient robustness issues, thereby failing to
fully retain or exploit long-term knowledge while being prone to cause severe
error accumulation. In this paper, we propose a novel Continual Meta-Learning
approach with Bayesian Graph Neural Networks (CML-BGNN) that mathematically
formulates meta-learning as continual learning of a sequence of tasks. With
each task forming as a graph, the intra- and inter-task correlations can be
well preserved via message-passing and history transition. To remedy
topological uncertainty from graph initialization, we utilize Bayes by Backprop
strategy that approximates the posterior distribution of task-specific
parameters with amortized inference networks, which are seamlessly integrated
into the end-to-end edge learning. Extensive experiments conducted on the
miniImageNet and tieredImageNet datasets demonstrate the effectiveness and
efficiency of the proposed method, improving the performance by 42.8% compared
with state-of-the-art on the miniImageNet 5-way 1-shot classification task.

提出了一种新颖的连续元学习方法，使用贝叶斯图神经网络 (CML-BGNN) 将元学习数学公式化为一系列任务的连续学习，在图形上保留任务内部和任务之间的相关性，利用 Amortized inference networks 解决了图形初始化的拓扑不确定性，提高了 minImageNet  5-way 1-shot 分类任务的分类性能。