39 research outputs found
Recurrent Gaussian processes
We define Recurrent Gaussian Processes (RGP) models, a general family of
Bayesian nonparametric models with recurrent GP priors which are able to learn
dynamical patterns from sequential data. Similar to Recurrent Neural Networks
(RNNs), RGPs can have different formulations for their internal states,
distinct inference methods and be extended with deep structures. In such
context, we propose a novel deep RGP model whose autoregressive states are
latent, thereby performing representation and dynamical learning
simultaneously. To fully exploit the Bayesian nature of the RGP model we
develop the Recurrent Variational Bayes (REVARB) framework, which enables
efficient inference and strong regularization through coherent propagation of
uncertainty across the RGP layers and states. We also introduce a RGP extension
where variational parameters are greatly reduced by being reparametrized
through RNN-based sequential recognition models. We apply our model to the
tasks of nonlinear system identification and human motion modeling. The
promising obtained results indicate that our RGP model maintains its highly
flexibility while being able to avoid overfitting and being applicable even
when larger datasets are not available
Recurrent Gaussian Processes
We define Recurrent Gaussian Processes (RGP) models, a general family of Bayesian nonparametric models with recurrent GP priors which are able to learn dynamical patterns from sequential data. Similar to Recurrent Neural Networks (RNNs), RGPs can have different formulations for their internal states, distinct inference methods and be extended with deep structures. In such context, we propose a novel deep RGP model whose autoregressive states are latent, thereby performing representation and dynamical learning simultaneously. To fully exploit the Bayesian nature of the RGP model we develop the Recurrent Variational Bayes (REVARB) framework, which enables efficient inference and strong regularization through coherent propagation of uncertainty across the RGP layers and states. We also introduce a RGP extension where variational parameters are greatly reduced by being reparametrized through RNN-based sequential recognition models. We apply our model to the tasks of nonlinear system identification and human motion modeling. The promising obtained results indicate that our RGP model maintains its highly flexibility while being able to avoid overfitting and being applicable even when larger datasets are not available
How priors of initial hyperparameters affect Gaussian process regression models
The hyperparameters in Gaussian process regression (GPR) model with a
specified kernel are often estimated from the data via the maximum marginal
likelihood. Due to the non-convexity of marginal likelihood with respect to the
hyperparameters, the optimization may not converge to the global maxima. A
common approach to tackle this issue is to use multiple starting points
randomly selected from a specific prior distribution. As a result the choice of
prior distribution may play a vital role in the predictability of this
approach. However, there exists little research in the literature to study the
impact of the prior distributions on the hyperparameter estimation and the
performance of GPR. In this paper, we provide the first empirical study on this
problem using simulated and real data experiments. We consider different types
of priors for the initial values of hyperparameters for some commonly used
kernels and investigate the influence of the priors on the predictability of
GPR models. The results reveal that, once a kernel is chosen, different priors
for the initial hyperparameters have no significant impact on the performance
of GPR prediction, despite that the estimates of the hyperparameters are very
different to the true values in some cases
Doubly Stochastic Variational Inference for Deep Gaussian Processes
Gaussian processes (GPs) are a good choice for function approximation as they
are flexible, robust to over-fitting, and provide well-calibrated predictive
uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of
GPs, but inference in these models has proved challenging. Existing approaches
to inference in DGP models assume approximate posteriors that force
independence between the layers, and do not work well in practice. We present a
doubly stochastic variational inference algorithm, which does not force
independence between layers. With our method of inference we demonstrate that a
DGP model can be used effectively on data ranging in size from hundreds to a
billion points. We provide strong empirical evidence that our inference scheme
for DGPs works well in practice in both classification and regression.Comment: NIPS 201