Further, we introduce sparseness in the eigenbasis by variational learning of the spherical harmonic phases.
The need for matrix decompositions (inverses) is often named as a major impediment to scaling Gaussian process (GP) models, even in efficient approximations.
This results in models that can either be seen as neural networks with improved uncertainty prediction or deep Gaussian processes with increased prediction accuracy.
GPflux is compatible with and built on top of the Keras deep learning eco-system.
We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations.
Approximate inference in complex probabilistic models such as deep Gaussian processes requires the optimisation of doubly stochastic objective functions.
One obstacle to the use of Gaussian processes (GPs) in large-scale problems, and as a component in deep learning system, is the need for bespoke derivations and implementations for small variations in the model or inference.
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint.
We present a variational approximation for a wide range of GP models that does not require a matrix inverse to be performed at each optimisation step.
As we demonstrate in our experiments, the factorisation between latent system states and transition function can lead to a miscalibrated posterior and to learning unnecessarily large noise terms.
Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings.
Banded matrices can be used as precision matrices in several models including linear state-space models, some Gaussian processes, and Gaussian Markov random fields.
We also demonstrate that our fully Bayesian approach improves on dropout-based Bayesian deep learning methods in terms of uncertainty and marginal likelihood estimates.
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process.
Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space.
The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored.
We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images.
In this paper, we introduce the pseudo-extended MCMC method as a simple approach for improving the mixing of the MCMC sampler for multi-modal posterior distributions.
Alternatively, state-of-the-art joint modeling techniques can be used for jointly modeling the longitudinal and event data and compute event probabilities conditioned on the longitudinal observations.
To address this challenge, we impose a structured Gaussian variational posterior distribution over the latent states, which is parameterised by a recognition model in the form of a bi-directional recurrent neural network.
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes.
GPflow is a Gaussian process library that uses TensorFlow for its core computations and Python for its front end.
This paper simultaneously addresses these, using a variational approximation to the posterior which is sparse in support of the function but otherwise free-form.
The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction.
We then discuss augmented index sets and show that, contrary to previous works, marginal consistency of augmentation is not enough to guarantee consistency of variational inference with the original model.
Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning.
In this work, we present an extension of Gaussian process (GP) models with sophisticated parallelization and GPU acceleration.
In this publication, we combine two Bayesian non-parametric models: the Gaussian Process (GP) and the Dirichlet Process (DP).
We present a general method for deriving collapsed variational inference algorithms for probabilistic models in the conjugate exponential family.