论文标题
使用高斯工艺混合物过渡分布的自回旋密度建模
Autoregressive Density Modeling with the Gaussian Process Mixture Transition Distribution
论文作者
论文摘要
在存在嘈杂和异质的非线性动力学的情况下，我们开发了用于过渡密度近似的混合模型以及软模型的选择。我们的模型建立在连续状态空间的高斯混合物过渡分布（MTD）模型上，扩展了使用高斯工艺（GP）先验建模的非线性函数的组件均值。当几个混合组件活跃时，所得模型会灵活地捕获非线性和异质滞后依赖性，当几个组件活跃时，可以识别低阶非线性依赖性，同时推断相关的滞后，并且在多个且竞争的单延线模型上平均以量化/传播不确定的单LAG模型。混合物重量的稀疏性诱导先验有助于选择活性滞后的子集。分层模型规范遵循GP回归和MTD模型的惯例，承认了方便的Gibbs采样方案以进行后推理。我们通过两个模拟和两个实时序列展示了所提出的模型的性质，强调了依赖滞后的过渡密度和模型选择的近似。在大多数情况下，该模型果断地恢复了重要功能。提出的模型提供了一个简单而灵活的框架，可保留MTD模型类的有用和区分特征。
We develop a mixture model for transition density approximation, together with soft model selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our model builds on the Gaussian mixture transition distribution (MTD) model for continuous state spaces, extending component means with nonlinear functions that are modeled using Gaussian process (GP) priors. The resulting model flexibly captures nonlinear and heterogeneous lag dependence when several mixture components are active, identifies low-order nonlinear dependence while inferring relevant lags when few components are active, and averages over multiple and competing single-lag models to quantify/propagate uncertainty. Sparsity-inducing priors on the mixture weights aid in selecting a subset of active lags. The hierarchical model specification follows conventions for both GP regression and MTD models, admitting a convenient Gibbs sampling scheme for posterior inference. We demonstrate properties of the proposed model with two simulated and two real time series, emphasizing approximation of lag-dependent transition densities and model selection. In most cases, the model decisively recovers important features. The proposed model provides a simple, yet flexible framework that preserves useful and distinguishing characteristics of the MTD model class.
