Variational Gaussian Process State-Space Models
نویسندگان
چکیده
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.
منابع مشابه
The Variational Coupled Gaussian Process Dynamical Model
We present a full variational treatment of the Coupled Gaussian Process Dynamical Model (CGPDM), which is a non-parametric, modular dynamical movement primitive model. Our work builds on similar developments in Gaussian state-space models, but we obviate the need for sampling, which results in a fast deterministic approximation for the posterior of latent states. We illustrate the performance o...
متن کاملDirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach
We describe two related models to cluster multidimensional time-series under the assumption of an underlying linear Gaussian dynamical process. In the first model, times-series are assigned to the same cluster when they show global similarity in their dynamics, while in the second model times-series are assigned to the same cluster when they show simultaneous similarity. Both models are based o...
متن کاملVariational Inference for Gaussian Process Models with Linear Complexity
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of complex functions. In this work, we propose a novel variational Gaussian proc...
متن کاملProbabilistic Recurrent State-Space Models
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g., LSTMs) proved extremely successful in modeling complex timeseries data. Fully probabilistic SSMs, however, unfortunately often prove hard to train, even for smaller problems. To overcome this limitation, we propose a scalabl...
متن کاملApproximate inference for state-space models
This thesis is concerned with state estimation in partially observed diffusion processes with discrete time observations. This problem can be solved exactly in a Bayesian framework, up to a set of generally intractable stochastic partial differential equations. Numerous approximate inference methods exist to tackle the problem in a practical way. This thesis introduces a novel deterministic app...
متن کامل