title: Online Bayesian Nonparametric Mixture Models via Regression
Creators: name: Kang, An
Publisher: name: University of Kent
Year: 2018

description: Sensors are widely used in modern industrial systems as well as consumer devices, such as food production, energy transportation and nuclear power plant. The sensors of interest in this project from an engineering company are associated with industrial control systems, where high precision is the dominant concern. Due to manufacturing variation, sensors manufactured from the same production line are non-identical. Therefore, each sensor needs to be characterised via parameter estimation to achieve a high precision or accuracy before sending to the end users. The classical linear regression model has been adopted in current industry procedure, which requires a certain number of measurements per device to achieve the required level of accuracy. The aim of the project is, under guarantee of the required level of accuracy, to use the available information and advanced statistical models to reduce the number of measurements needed per sensor, and hence reduce both costs and time for the characterisation process. To achieve this, a Bayesian linear model with Dirichlet process mixture prior (BL-DPMP) is proposed, where the Bayesian linear regression presents the relationship between the response variable and the covariates demonstrated to be appropriate by the company, and the regression coefficients are modelled by a Dirichlet process mixture (DPM) model. The idea here is to apply the DPM model to the historical information from similar sensors to provide adequate prior information to the linear regression model in order to compensate the current characterising sensor with block missing measurements, at the same time to maintain the required level of accuracy. The slice sampling scheme based on the full conditional posteriors of hyperparameters is used to update the parameters in the DPM model. Also, a generalised Dirichlet process mixture regression model is proposed with a data-driven prediction procedure to deal with the considered situation. By reducing the number of measurements required per sensor, we could drastically reduce the characterisation period. However, two proposed approaches are quite computationally intensive, which counteract the time saved from collecting a fewer number of measurements. Hence, there is a clearly pressing need for dramatically faster alternatives. A hybrid Variational Bayes (HVB) procedure following a greedy searching scheme is proposed, which can dramatically reduce the computational time, at the same time provide highly accurate approximations of the exact posterior distributions. The ultimate goal of this project is to implement the proposed advanced statistical model in the production line, where the model can be executed within seconds (online). An optimal permutation sequential (OPS) algorithm for the DPM model is proposed, which differs from MCMC algorithms. The idea is to draw approximate independent and identically distributed samples from the posterior distribution of the latent allocations, and to draw samples from the weights and locations conditional on the allocations. Hence, independent draws are taken from the posterior distribution, which allow us to take independent samples from the predictive distribution. The OPS algorithm requires only a single run which the computational costs of a few seconds. We present examples to show model performance on simulated and real datasets. It is worth noting that the proposed Bayesian linear model with Dirichlet process mixture prior together with the OPS algorithm is under the testing stage of being implemented in our industrial partner's production line. This research acts as the underpinning work and contributes to a potential impact case for the Research Excellence Framework (REF) 2021.