IEEE Trans Neural Netw Learn Syst. 2015 Jan;26(1):70-83. doi: 10.1109/TNNLS.2014.2311073.
In this paper, we propose a Gaussian process (GP) model for analysis of nonlinear time series. Formulation of our model is based on the consideration that the observed data are functions of latent variables, with the associated mapping between observations and latent representations modeled through GP priors. In addition, to capture the temporal dynamics in the modeled data, we assume that subsequent latent representations depend on each other on the basis of a hidden Markov prior imposed over them. Derivation of our model is performed by marginalizing out the model parameters in closed form using GP priors for observation mappings, and appropriate stick-breaking priors for the latent variable (Markovian) dynamics. This way, we eventually obtain a nonparametric Bayesian model for dynamical systems that accounts for uncertainty in the modeled data. We provide efficient inference algorithms for our model on the basis of a truncated variational Bayesian approximation. We demonstrate the efficacy of our approach considering a number of applications dealing with real-world data, and compare it with the related state-of-the-art approaches.
在本文中，我们提出了一种用于分析非线性时间序列的高斯过程 (GP) 模型。我们模型的构建基于以下考虑：观测数据是潜在变量的函数，观测值和潜在表示之间的相关映射通过 GP 先验进行建模。此外，为了捕捉建模数据中的时间动态，我们假设后续的潜在表示相互依赖，这是基于施加在它们之上的隐马尔可夫先验。通过使用观测映射的 GP 先验和适当的打破潜在变量（马尔可夫）动态的 stick-breaking 先验来对模型参数进行闭形式的边缘化，从而最终得到一个用于动态系统的非参数贝叶斯模型，该模型考虑了建模数据中的不确定性。我们基于截断变分贝叶斯近似为我们的模型提供了高效的推断算法。我们考虑了一些涉及真实数据的应用，展示了我们方法的有效性，并将其与相关的最先进方法进行了比较。
