Fast Multi-Output Relevance Vector Regression

Ha, Youngmin; Zhang, Hai

doi:10.2139/ssrn.3376638

Cited by 3 publications

(5 citation statements)

References 9 publications

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“…Thayananthan, et al [33] extended RVM to multi-output relevance vector regression (MRVR); however, it still has the limitation of low computational efficiency. The FMRVR used in this paper is a fast version of the MRVR proposed by Ha [34]. The kernel parameter and input lag are crucial in the use of FMRVR.…”

Section: The Proposed Methodsmentioning

confidence: 99%

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Multi-Step-Ahead Carbon Price Forecasting Based on Variational Mode Decomposition and Fast Multi-Output Relevance Vector Regression Optimized by the Multi-Objective Whale Optimization Algorithm

et al. 2019

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The accurate and stable forecasting of carbon prices is vital for governors to make policies and essential for market participants to make investment decisions, which is important for promoting the development of carbon markets and reducing carbon emissions in China. However, it is challenging to improve the carbon price forecasting accuracy due to its non-linearity and non-stationary characteristics, especially in multi-step-ahead forecasting. In this paper, a hybrid multi-step-ahead forecasting model based on variational mode decomposition (VMD), fast multi-output relevance vector regression (FMRVR), and the multi-objective whale optimization algorithm (MOWOA) is proposed. VMD is employed to extract the primary mode for the carbon price. Then, FMRVR, which is used as the forecasting module, is built on the preprocessed data. To achieve high accuracy and stability, the MOWOA is utilized to optimize the kernel parameter and input the lag of the FMRVR. The proposed hybrid forecasting model is applied to carbon price series from three major regional carbon emission exchanges in China. Results show that the proposed VMD-FMRVR-MOWOA model achieves better performance compared to several other multi-output models in terms of forecasting accuracy and stability. The proposed model can be a potential and effective technique for multi-step-ahead carbon price forecasting in China’s three major regional emission exchanges.

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Section: The Proposed Methodsmentioning

confidence: 99%

“…Thayananthan [42] and Thayananthan et al [33] extended the RVM to the MRVR, which has the limitation of low computational efficiency. To overcome this limitation, Ha [34] proposed the FMRVR to decrease the time complexity of the MRVR.…”

Section: Fast Multi-output Relevance Vector Regression (Fmrvr)mentioning

confidence: 99%

Multi-Step-Ahead Carbon Price Forecasting Based on Variational Mode Decomposition and Fast Multi-Output Relevance Vector Regression Optimized by the Multi-Objective Whale Optimization Algorithm

et al. 2019

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“…where 𝛼 𝑛𝑒𝑤 and 𝐶 𝑛𝑒𝑤 denotes their updated quantity. The change in 𝐿(𝛼, 𝛺) depends on whether 𝛼 𝑖 is reestimated or added or deleted, and can be respectively represented as [25],…”

Section: A Multivariate Relevance Vector Regression (Mvrvr)mentioning

confidence: 99%

“…To deal with this, multivariate RVR (MVRVR) is proposed for performing multi-output nonlinear regression [24]. The computational efficiency of the algorithm is improved further by employing matrix normal distribution in place of multivariate normal distribution [25]. The advantage of MVRVR is considering the relationship among the target samples and the fundamental correlation between the input and target samples.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Assisted Hybrid Electromagnetic Modeling Framework and Its Applications to UWB MIMO Antennas

et al. 2023

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Machine learning (ML) has gained recognition as an efficient and robust technique to realize the solution of electromagnetic forward and inverse problems. This article introduces a hybrid ML framework that simultaneously acts as a forward and inverse model based on a mode input. Multivariate relevance vector regression (MVRVR) is adopted for implementing the hybrid ML model. MVRVR models for forward and inverse modeling are also presented. In addition, three hybrid ML models based on support vector regression (SVR), Gaussian process regression (GPR), and artificial neural network (ANN) are also implemented and a thorough comparative analysis between these ML models with the proposed MVRVR model is investigated to verify its accuracy. The proposed hybrid framework can be used to replace the requirements of the two separate models for solving forward and inverse problems. Two examples of ultrawideband (UWB) MIMO antennas are employed to validate the effectiveness of the proposed modeling framework.INDEX TERMS Machine learning, MIMO antenna, multivariate relevance vector regression (MVRVR), ultra-wideband (UWB)

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“…The RVM, which was proposed by Tipping (2001), is a sparse probabilistic model based on the Bayesian framework. The M-RVM was established after the RVM by Thayananthana et al (2008) for multi-output regression problems, and then a faster and more practicable M-RVM algorithm that uses a matrix normal distribution to model the correlated outputs was proposed by Ha and Zhang (2019). To improve the computing accuracy, the MMRVM is established by introducing a mixed kernel function in this research.…”

Section: Multi-output Relevance Vector Machinementioning

confidence: 99%

Adaptive parameter inversion analysis method of rockfill dam based on harmony search algorithm and mixed multi-output relevance vector machine

Cheng

Ran

2020

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Purpose To improve the efficiency, accuracy and adaptivity of the parameter inversion analysis method of a rockfill dam, this study aims to establish an adaptive model based on a harmony search algorithm (HS) and a mixed multi-output relevance vector machine (MMRVM). Design/methodology/approach By introducing the mixed kernel function, the MMRVM can accurately simulate the nonlinear relationship between the material parameters and dam settlement. Therefore, the finite element method with time consumption can be replaced by the MMRVM. Because of its excellent global search capability, the HS is used to optimize the kernel parameters of the MMRVM and the material parameters of a rockfill dam. Findings Because the parameters of the HS and the variation range of the MMRVM parameters are relatively fixed, the HS-MMRVM can imbue the inversion analysis with adaptivity; the number of observation points required and the robustness of the HS-MMRVM are analyzed. An application example involving a concrete-faced rockfill dam shows that the HS-MMRVM exhibits high accuracy and high speed in the parameter inversion analysis of static and creep constitutive models. Practical implications The applicability of the HS-MMRVM in hydraulic engineering is proved in this paper, which should further validate in inversion problems of other fields. Originality/value An adaptive inversion analysis model is established to avoid the parameters of traditional methods that need to be set by humans, which strongly affect the inversion analysis results. By introducing the mixed kernel function, the MMRVM can accurately simulate the nonlinear relationship between the material parameters and dam settlement. To reduce the data dimensions and verify the model’s robustness, the number of observation points required for inversion analysis and the acceptable degree of noise are determined. The confidence interval is built to monitor dam settlement and provide the foundation for dam monitoring and reservoir operation management.

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Fast Multi-Output Relevance Vector Regression

Cited by 3 publications

References 9 publications

Multi-Step-Ahead Carbon Price Forecasting Based on Variational Mode Decomposition and Fast Multi-Output Relevance Vector Regression Optimized by the Multi-Objective Whale Optimization Algorithm

Multi-Step-Ahead Carbon Price Forecasting Based on Variational Mode Decomposition and Fast Multi-Output Relevance Vector Regression Optimized by the Multi-Objective Whale Optimization Algorithm

Machine Learning Assisted Hybrid Electromagnetic Modeling Framework and Its Applications to UWB MIMO Antennas

Adaptive parameter inversion analysis method of rockfill dam based on harmony search algorithm and mixed multi-output relevance vector machine

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