Lagrangian support vector regression via unconstrained convex minimization

Balasundaram, S.; Gupta, Deepak; Kapil,

doi:10.1016/j.neunet.2013.12.003

Cited by 35 publications

(5 citation statements)

References 17 publications

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“…As an advantage, SVR can be applied to not only linear regression functions but also nonlinear regression functions. Only the dot product of two vectors is required to solve the Lagrangian methods to obtain ( ) f x ; thus, this allows the determination of the dot product of two vectors in high dimensions that can be represented linearly by kernel functions [51,52]. There are several kernel functions such as the radial basis, polynomial, and sigmoid functions [53].…”

Section: Svrmentioning

confidence: 99%

National-scale electricity peak load forecasting: Traditional, machine learning, or hybrid model?

Lee

Cho

2022

Energy

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Section: Svrmentioning

confidence: 99%

National-scale electricity peak load forecasting: Traditional, machine learning, or hybrid model?

Lee

Cho

2022

Energy

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“…Therefore, K‐StoNet is trained by solving a series of convex optimization problems . Note that the minimization in Equation (13) is known as a convex quadratic programming problem (Vapnik, 2000, 2013). Although solving the convex optimization problems is more expensive than a single gradient update, the IRO algorithm converges very fast, usually within tens of iterations. The major computational cost of K‐StoNet comes from the SVR step when the sample size is large.…”

Section: A Kernel‐expanded Stochastic Neural Networkmentioning

confidence: 99%

A Kernel-Expanded Stochastic Neural Network

Sun

Liang

2022

Journal of the Royal Statistical Society Series B: Statistical Methodology

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The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we propose the so-called kernel-expanded stochastic neural network (K-StoNet) model, which incorporates support vector regression as the first hidden layer and reformulates the neural network as a latent variable model. The former maps the input vector into an infinite dimensional feature space via a radial basis function kernel, ensuring the absence of local minima on its training loss surface. The latter breaks the high-dimensional non-convex neural network training problem into a series of low-dimensional convex optimization problems, and enables its prediction uncertainty easily assessed. The K-StoNet can be easily trained using the imputation-regularized optimization algorithm. Compared to traditional deep neural networks, K-StoNet possesses a theoretical guarantee to asymptotically converge to the global optimum and enables the prediction uncertainty easily assessed. The performances of the new model in training, prediction and uncertainty quantification are illustrated by simulated and real data examples.

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“…The system input and output of this flexible robot arm are the measured reaction torque and the acceleration, respectively [27]. There are two attributes in this flexible robot arm example, and all of the 1024 pairs of data are described in Figure 2.…”

Section: Robot Arm Examplementioning

confidence: 99%

Time Series Prediction Based on Adaptive Weight Online Sequential Extreme Learning Machine

Huang

Lü

2017

Applied Sciences

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A novel adaptive weight online sequential extreme learning machine (AWOS-ELM) is proposed for predicting time series problems based on an online sequential extreme learning machine (OS-ELM) in this paper. In real-world online applications, the sequentially coming data chunk usually possesses varying confidence coefficients, and the data chunk with a low confidence coefficient tends to mislead the subsequent training process. The proposed AWOS-ELM can improve the training process by accessing the confidence coefficient adaptively and determining the training weight accordingly. Experiments on six time series prediction data sets have verified that the AWOS-ELM algorithm performs better in generalization performance, stability, and prediction ability than the OS-ELM algorithm. In addition, a real-world mechanical system identification problem is considered to test the feasibility and efficacy of the AWOS-ELM algorithm.

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Lagrangian support vector regression via unconstrained convex minimization

Cited by 35 publications

References 17 publications

National-scale electricity peak load forecasting: Traditional, machine learning, or hybrid model?

National-scale electricity peak load forecasting: Traditional, machine learning, or hybrid model?

A Kernel-Expanded Stochastic Neural Network

Time Series Prediction Based on Adaptive Weight Online Sequential Extreme Learning Machine

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