Quantile Regression Neural Networks: A Bayesian Approach

Jantre, Sanket; Bhattacharya, Shrijita; Maiti, Tapabrata

doi:10.1007/s42519-021-00189-w

Cited by 8 publications

(3 citation statements)

References 33 publications

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“…The gas [SiO(g)] formed in this area rises and is dissolved in the slag as silicon dioxide (SiO2) or in the hot metal as silicon. The second possibility is the reduction of silicon oxide [SiO(g)] by carbon dissolved in the hot metal [40]- [43]. There is also the possibility of reoxidation of silicon in the hot metal when the cast iron chemically interacts with iron oxide (FeO) dissolved in the slag according to Equation ( 4) and ( 5) and Equation (6).…”

Section: Resultsmentioning

confidence: 99%

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Prediction of silicon content in the hot metal using Bayesian networks and probabilistic reasoning

Cardoso

Felice

2021

Int. J. Adv. Intell. Informatics

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The blast furnace is the principal method of producing cast iron. In the production of cast iron, the control of silicon is vital because this impurity is harmful to almost all steels. Artificial neural networks with Bayesian regularization are more robust than traditional back-propagation networks and can reduce or eliminate the need for tedious cross-validation. Bayesian regularization is a mathematical process that converts a nonlinear regression into a "well-posed" statistical problem in the manner of ridge regression. The main objective of this work was to develop an artificial neural network to predict silicon content in hot metal by varying the number of neurons in the hidden layer by 10, 20, 25, 30, 40, 50, 75, and 100 neurons. The results show that all neural networks converged and presented reliable results, neural networks with 20, 25, and 30 neurons showed the best overall results. However, In short, Bayesian neural networks can be used in practice because the actual values correlate excellently with the values calculated by the neural network.

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Section: Resultsmentioning

confidence: 99%

“…In this context, the main objective of this work was to build the source code of a Bayesian artificial neural network to determine the number of neurons with the best results for predicting the silicon content in cast iron, varying the number of neurons in the hidden layer by 10,20,25,30,40,50, 75 and 100 neurons.…”

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confidence: 99%

Prediction of silicon content in the hot metal using Bayesian networks and probabilistic reasoning

Cardoso

Felice

2021

Int. J. Adv. Intell. Informatics

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“…Some authors have also proposed structured recipes for designing a network with dependent weights while ensuring that the weights are partially exchangeable. One particular way is to consider a scale mixture of Gaussians for the weight distribution [18,34,27,11,12]. Infinite-width limits of these networks with Gaussian scale mixture weights have also been studied, at least in part, by [23].…”

Section: Discussionmentioning

confidence: 99%

-Stable convergence of heavy-/light-tailed infinitely wide neural networks

Jung

Lee

et al. 2023

Adv. Appl. Probab.

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We consider infinitely wide multi-layer perceptrons (MLPs) which are limits of standard deep feed-forward neural networks. We assume that, for each layer, the weights of an MLP are initialized with independent and identically distributed (i.i.d.) samples from either a light-tailed (finite-variance) or a heavy-tailed distribution in the domain of attraction of a symmetric $\alpha$ -stable distribution, where $\alpha\in(0,2]$ may depend on the layer. For the bias terms of the layer, we assume i.i.d. initializations with a symmetric $\alpha$ -stable distribution having the same $\alpha$ parameter as that layer. Non-stable heavy-tailed weight distributions are important since they have been empirically seen to emerge in trained deep neural nets such as the ResNet and VGG series, and proven to naturally arise via stochastic gradient descent. The introduction of heavy-tailed weights broadens the class of priors in Bayesian neural networks. In this work we extend a recent result of Favaro, Fortini, and Peluchetti (2020) to show that the vector of pre-activation values at all nodes of a given hidden layer converges in the limit, under a suitable scaling, to a vector of i.i.d. random variables with symmetric $\alpha$ -stable distributions, $\alpha\in(0,2]$ .

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Data Mining and Machine Learning to Predict the Sulphur Content in the Hot Metal of a Coke-Fired Blast Furnace

Cardoso¹,

Felice²

2023

Communications in Computer and Information Science

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Quantile Regression Neural Networks: A Bayesian Approach

Cited by 8 publications

References 33 publications

Prediction of silicon content in the hot metal using Bayesian networks and probabilistic reasoning

Prediction of silicon content in the hot metal using Bayesian networks and probabilistic reasoning

-Stable convergence of heavy-/light-tailed infinitely wide neural networks

Data Mining and Machine Learning to Predict the Sulphur Content in the Hot Metal of a Coke-Fired Blast Furnace

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