Related papers: Monotonic Gaussian Process Flow
We consider the problem of computing the satisfaction probability of a formula for stochastic models with parametric uncertainty. We show that this satisfaction probability is a smooth function of the model parameters. This enables us to…
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…
We develop a Bayesian non-parametric framework based on multi-task Gaussian processes, appropriate for temporal shrinkage. We focus on a particular class of dynamic hierarchical models to obtain evidence-based knowledge of infectious…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
We propose a new method for automatically detecting monotonic input-output relationships from data using Gaussian Process (GP) models with virtual derivative observations. Our results on synthetic and real datasets show that the proposed…
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
We consider the problem of sequentially maximising an unknown function over a set of actions while ensuring that every sampled point has a function value below a given safety threshold. We model the function using kernel-based and Gaussian…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…
In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we…
This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes…
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…
Analyzing the underlying structure of multiple time-sequences provides insights into the understanding of social networks and human activities. In this work, we present the \emph{Bayesian nonparametric Poisson process allocation} (BaNPPA),…