迈向高斯过程状态空间模型的灵活性与可解释性
Towards Flexibility and Interpretability of Gaussian Process State-Space Model
AI总结：
针对标准GPSSM因初步核函数导致表示能力受限的问题，提出TGPSSM模型，利用参数化normalizing flow丰富GP先验，并结合可扩展变分推断与约束优化算法，提升了模型的灵活性、可解释性与推断性能。
摘要：
过去十年间，高斯过程状态空间模型（GPSSM）受到了广泛关注。然而，GPSSM研究中常用的标准GP及初步核函数（如平方指数核或Matérn核）限制了模型的表示能力，并大幅限制了其在复杂场景中的适用性。为解决此问题，我们提出了一类新的概率状态空间模型TGPSSM，它利用参数化normalizing flow来丰富标准GPSSM中的GP先验，从而实现更大的灵活性与表达能力。此外，我们提出了一种可扩展的变分推断算法，为潜在状态的变分分布提供了灵活且最优的结构。得益于稀疏GP表示和normalizing flow的双射特性，所提算法具有可解释性和计算高效性。而且，我们将约束优化框架融入算法中以增强状态空间表示能力并优化超参数，从而带来更优的学习与推断性能。在合成和真实数据集上的实验结果证实，所提TGPSSM优于几种state-of-the-art方法。配套源代码可在https://github.com/zhidilin/TGPSSM获取。
英文摘要：
The Gaussian process state-space model (GPSSM) has garnered considerable attention over the past decade. However, the standard GP with a preliminary kernel, such as the squared exponential kernel or Matérn kernel, that is commonly used in GPSSM studies, limits the model's representation power and substantially restricts its applicability to complex scenarios. To address this issue, we propose a new class of probabilistic state-space models called TGPSSMs, which leverage a parametric normalizing flow to enrich the GP priors in the standard GPSSM, enabling greater flexibility and expressivity. Additionally, we present a scalable variational inference algorithm that offers a flexible and optimal structure for the variational distribution of latent states. The proposed algorithm is interpretable and computationally efficient due to the sparse GP representation and the bijective nature of normalizing flow. Moreover, we incorporate a constrained optimization framework into the algorithm to enhance the state-space representation capabilities and optimize the hyperparameters, leading to superior learning and inference performance. Experimental results on synthetic and real datasets corroborate that the proposed TGPSSM outperforms several state-of-the-art methods. The accompanying source code is available at \url{https://github.com/zhidilin/TGPSSM}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
