Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAdaptive Inducing Points Selection For Gaussian Processes
163
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Gaussian Processes (textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting. cite{bui2017streaming} developed an efficient variational approach to train online GPs by using sparsity techniques: The whole set of observations is approximated by a smaller set of inducing points (textbf{IPs}) and moved around with new data. Both the number and the locations of the IPs will affect greatly the performance of the algorithm. In addition to optimizing their locations, we propose to adaptively add new points, based on the properties of the GP and the structure of the data.
rate research
Read More
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the great flexibility of multilayer models. In DGPs, given the inputs, the outputs of the layers are Gaussian distributions parameterized by their means and covariances. These layers are realized as Sparse GPs where the training data is approximated using a small set of pseudo points. In this work, we show that the computational cost of DGPs can be reduced with no loss in performance by using a separate, smaller set of pseudo points when calculating the layerwise variance while using a larger set of pseudo points when calculating the layerwise mean. This enabled us to train larger models that have lower cost and better predictive performance.
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to a linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e. a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.
We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together with fast but accurate posterior inference. We investigate several variations of the convolutional kernel, and apply it to MNIST and CIFAR-10, which have both been known to be challenging for Gaussian processes. We also show how the marginal likelihood can be used to find an optimal weighting between convolutional and RBF kernels to further improve performance. We hope that this illustration of the usefulness of a marginal likelihood will help automate discovering architectures in larger models.
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient Kalman filter-like recursions, resulting in algorithms whose computational and memory requirements scale linearly in the number of inducing points, whilst also enabling parallel parameter updates and stochastic optimisation. Under this paradigm, we derive a general site-based approach to approximate inference, whereby we approximate the non-Gaussian likelihood with local Gaussian terms, called sites. Our approach results in a suite of novel sparse extensions to algorithms from both the machine learning and signal processing literature, including variational inference, expectation propagation, and the classical nonlinear Kalman smoothers. The derived methods are suited to large time series, and we also demonstrate their applicability to spatio-temporal data, where the model has separate inducing points in both time and space.
Policy gradient reinforcement learning (RL) algorithms have achieved impressive performance in challenging learning tasks such as continuous control, but suffer from high sample complexity. Experience replay is a commonly used approach to improve sample efficiency, but gradient estimators using past trajectories typically have high variance. Existing sampling strategies for experience replay like uniform sampling or prioritised experience replay do not explicitly try to control the variance of the gradient estimates. In this paper, we propose an online learning algorithm, adaptive experience selection (AES), to adaptively learn an experience sampling distribution that explicitly minimises this variance. Using a regret minimisation approach, AES iteratively updates the experience sampling distribution to match the performance of a competitor distribution assumed to have optimal variance. Sample non-stationarity is addressed by proposing a dynamic (i.e. time changing) competitor distribution for which a closed-form solution is proposed. We demonstrate that AES is a low-regret algorithm with reasonable sample complexity. Empirically, AES has been implemented for deep deterministic policy gradient and soft actor critic algorithms, and tested on 8 continuous control tasks from the OpenAI Gym library. Ours results show that AES leads to significantly improved performance compared to currently available experience sampling strategies for policy gradient.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
