Prediction intervals for industrial data with incomplete input using kernel-based dynamic Bayesian networks
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Reliable prediction intervals (PIs) construction for industrial time series is substantially significant for decision-making in production practice. Given the industrial data feature of high level noises and incomplete input, a high order dynamic Bayesian network (DBN)-based PIs construction method for industrial time series is proposed in this study. For avoiding to designate the amount and type of the basis functions in advance, a linear combination of kernel functions is designed to describe the relationships between the nodes in the network, and a learning method based on the scoring criterion—the sparse Bayesian score, is then reported to acquire suitable model parameters such as the weights and the variances. To verify the performance of the proposed method, two types of time series which are the classical Mackey-Glass data mixed by additive noises and a real-world industrial data are employed. The results indicate the effectiveness of our proposed method for the PIs construction of the industrial data with incomplete input.
KeywordsPrediction intervals Dynamic Bayesian network Kernel Sparse Bayesian learning Incomplete input
This work is supported by the National Natural Sciences Foundation of China (No. 61273037, 61304213, 61473056, 61533005, 61522304, U1560102), the National Sci-Tech Support Plan (No. 2015BAF22B01) and Fundamental Research Funds for the Central Universities (DUT15YQ113).
- Cruz-Ramírez N, Acosta-Mesa HG, Barrientos-Martínez RE et al (2006) How good are the Bayesian information criterion and the minimum description length principle for model selection? A Bayesian network analysis. In: Gelbukh A, Reyes-Garcia CA (eds) Advances in artificial intelligence. Springer, Heidelberg, pp 494–504Google Scholar
- Fung R, Chang KC (1990) Weighting and integrating evidence for stochastic simulation in Bayesian networks. In: Bonissone PP, Henrion M, Kanal LN, Lemmer JF (eds) Uncertainty in Artificial Intelligence, 5. Elsevier, pp 208–219Google Scholar
- Jaeger H (2002) Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the “echo state network” approach. GMD Report 159, German National Research Center for Information TechnologyGoogle Scholar
- Murphy KP (2002) Dynamic Bayesian networks: representation, inference and learning. University of California, BerkeleyGoogle Scholar
- Nix DA, Weigend AS (1994) Estimating the mean and variance of the target probability distribution. Computational Intelligence. In: 1994 IEEE World Congress on Computational Intelligence 1: 55–60Google Scholar
- Regnier-Coudert O, McCall J (2012) An island model genetic algorithm for Bayesian network structure learning. In: 2012 IEEE Congress on Evolutionary Computation, 1–8Google Scholar
- Tipping ME (2005) Variational relevance vector machine. U.S. PatentGoogle Scholar
- Tipping ME, Faul AC (2003) Fast marginal likelihood maximisation for sparse Bayesian models. In: 2003 Proceedings of the ninth international workshop on artificial intelligence and statistics. 1Google Scholar