The Bayesian analysis of neural networks is diicult because the prior over functions has a complex form, leading to implementations that either make approximations or use Monte Carlo integration techniques. In this paper I investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis to be carried out exactly using matrix operations. The method has...

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 ...

We propose a powerful prediction algorithm built upon Gaussian processes (GPs). They are particularly useful for their flexibility, facilitating accurate prediction even in the absence of strong physical models. GPs further allow us to work within a complete Bayesian probabilistic framework. As such, we show how the hyperparameters of our system can be marginalised by use of Bayesian Monte Carl...

A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Differential privacy is a framework which allows algorithms to have provable privacy guarantees. Gaussian processes are a widely used approach for dealing with uncertainty in functions. This paper explores differentially private mechanisms for Gaussian processes. We compare...

This paper studies construction of quantum Gaussian processes based on ordinary Gaussian processes through their reproducing kernel Hilbert spaces, and investigate the relationship between the stochastic properties of the quantum Gaussian processes and the base Gaussian processes. In particular, we construct quantum Brownian bridges and quantum Ornstein-Uhlenbeck processes. Non-commutative stoc...