Derivative observations in Gaussian Process models of dynamic systems

Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data. 1)It allows us to combine derivative information, and associated uncertainty with normal function observations into the learning and inference process. This derivative information can be in the form of priors specified by an expert or identified from perturbation data close to equilibrium. 2) It allows a seamless fusion of multiple local linear models in a consistent manner, inferring consistent models and ensuring that integrability constraints are met. 3) It improves dramatically the computational efficiency of Gaussian process models for dynamic system identification, by summarising large quantities of near-equilibrium data by a handful of linearisations, reducing the training size - traditionally a problem for Gaussian process models

Determination of the quark-gluon string parameters from the data on pp, pA and AA collisions at wide energy range using Bayesian Gaussian Process Optimization

Bayesian Gaussian Process Optimization can be considered as a method of the determination of the model parameters, based on the experimental data. In the range of soft QCD physics, the processes of hadron and nuclear interactions require using phenomenological models containing many parameters. In order to minimize the computation time, the model predictions can be parameterized using Gaussian Process regression, and then provide the input to the Bayesian Optimization. In this paper, the Bayesian Gaussian Process Optimization has been applied to the Monte Carlo model with string fusion. The parameters of the model are determined using experimental data on multiplicity and cross section of pp, pA and AA collisions at wide energy range. The results provide important constraints on the transverse radius of the quark-gluon string ($r_{str}$) and the mean multiplicity per rapidity from one string ($\mu_0$).Comment: 9 pages, 5 figures, proc. XIIIth Quark Confinement and the Hadron Spectru

Data fusion with Gaussian processes for estimation of environmental hazard events

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordThe data that support the findings of this study are openly available at https://wisc.climate.copernicus.eu/wisc/#/ help/products#stormtrack_download, WISC (2019).Environmental hazard events such as extra-tropical cyclones or windstorms that develop in the North Atlantic can cause severe societal damage. Environmental hazard is quantified by the hazard footprint, a spatial area describing potential damage. However, environmental hazards are never directly observed, so estimation of the footprint for any given event is primarily reliant on station observations (e.g., wind speed in the case of a windstorm event) and physical model hindcasts. Both data sources are indirect measurements of the true footprint, and here we present a general statistical framework to combine the two data sources for estimating the underlying footprint. The proposed framework extends current data fusion approaches by allowing structured Gaussian process discrepancy between physical model and the true footprint, while retaining the elegance of how the "change of support" problem is dealt with. Simulation is used to assess the practical feasibility and efficacy of the framework, which is then illustrated using data on windstorm ImogenNatural Environment Research Council (NERC

Fast hierarchical fusion model based on least squares B-splines approximation

With manufacturing shifting from traditional products to high value products, the complexity and accuracy of the products are increasing in order to reduce energy costs, create friendly environment and better health care. Structured surfaces, freeform surfaces, and other functional engineering surfaces are becoming the core part of high value manufacturing products. However, measurement of these surfaces is becoming very difficult due to instrumental limitations including measurement range, speed, resolution and accuracy. Multi-instruments/sensors measurement are now being developed for freeform and structured surface assessment, which requires the fusion of the data into a unified system to achieve larger dynamic measurements with greater reliability. This paper discusses the process of combining data from several information sources (instruments/sensors) into a common representational format and the surface topography can be reconstructed using Gaussian processes and B-spline techniques. In this paper the Gaussian process model is extended in order to take into account the uncertainty propagation and a new data fusion model based on least squares B-splines that drastically reduce the computational time are presented. The results are validated by two for freeform surface measurements

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

Hierarchical Bayesian modelling of gene expression time series across irregularly sampled replicates and clusters.

BACKGROUND: Time course data from microarrays and high-throughput sequencing experiments require simple, computationally efficient and powerful statistical models to extract meaningful biological signal, and for tasks such as data fusion and clustering. Existing methodologies fail to capture either the temporal or replicated nature of the experiments, and often impose constraints on the data collection process, such as regularly spaced samples, or similar sampling schema across replications. RESULTS: We propose hierarchical Gaussian processes as a general model of gene expression time-series, with application to a variety of problems. In particular, we illustrate the method's capacity for missing data imputation, data fusion and clustering.The method can impute data which is missing both systematically and at random: in a hold-out test on real data, performance is significantly better than commonly used imputation methods. The method's ability to model inter- and intra-cluster variance leads to more biologically meaningful clusters. The approach removes the necessity for evenly spaced samples, an advantage illustrated on a developmental Drosophila dataset with irregular replications. CONCLUSION: The hierarchical Gaussian process model provides an excellent statistical basis for several gene-expression time-series tasks. It has only a few additional parameters over a regular GP, has negligible additional complexity, is easily implemented and can be integrated into several existing algorithms. Our experiments were implemented in python, and are available from the authors' website: http://staffwww.dcs.shef.ac.uk/people/J.Hensman/