Bayesian Neural Networks

Bishop, Christopher M.

doi:10.1590/s0104-65001997000200006

Cited by 47 publications

(27 citation statements)

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“…For each child, we calculated the posterior probability of belonging to each of the latent classes, and assigned children to their highest probability class. We compared the models using model evidence, a measure of model goodness-of-fit, to identify the most parsimonious model [41] .…”

Section: Methodsmentioning

confidence: 99%

Developmental Profiles of Eczema, Wheeze, and Rhinitis: Two Population-Based Birth Cohort Studies

et al. 2014

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Section: Methodsmentioning

confidence: 99%

Developmental Profiles of Eczema, Wheeze, and Rhinitis: Two Population-Based Birth Cohort Studies

et al. 2014

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“…To achieve a good balance between bias and variance in order to avoid overfitting phenomena by training data, it is an advisable choice for a function smooth network [19].…”

Section: Markov Chain Hybrid Monte Carlo Methodsmentioning

confidence: 99%

“…Then, the interpolating function is chosen using the maximum likelihood criterion. In this sense, it has been demonstrated that in the case of an output noise independent from the input variables, the maximum likelihood criterion provides distorted results because it systematically underestimates the variance of the noise itself [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Real Estate Appraisals with Bayesian Approach and Markov Chain Hybrid Monte Carlo Method: An Application to a Central Urban Area of Naples

et al. 2017

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Abstract:This paper experiments an artificial neural networks model with Bayesian approach on a small real estate sample. The output distribution has been calculated operating a numerical integration on the weights space with the Markov Chain Hybrid Monte Carlo Method (MCHMCM). On the same real estate sample, MCHMCM has been compared with a neural networks model (NNs), traditional multiple regression analysis (MRA) and the Penalized Spline Semiparametric Method (PSSM). All four methods have been developed for testing the forecasting capacity and reliability of MCHMCM in the real estate field. The Markov Chain Hybrid Monte Carlo Method has proved to be the best model with an absolute average percentage error of 6.61%.

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“…A principled approach for solving this problem is Bayesian Neural Networks (see Vehtari & Lampinen (1999), Bishop (1997)). Prior distributions are placed on the neural network weights in Bayesian Neural Networks to consider the model uncertainty.…”

Section: Combination Of Neural Network Regression and Potts Clustering Modelmentioning

confidence: 99%

The Shallow Gibbs Network, Double Backpropagation and Differential Machine learning

Murua

Alahassa

2021

Preprint

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We have built a Shallow Gibbs Network model as a Random Gibbs Network Forest to reach the performance of the Multilayer feedforward Neural Network in a few numbers of parameters, and fewer backpropagation iterations. To make it happens, we propose a novel optimization framework for our Bayesian Shallow Network, called the {Double Backpropagation Scheme} (DBS) that can also fit perfectly the data with appropriate learning rate, and which is convergent and universally applicable to any Bayesian neural network problem. The contribution of this model is broad. First, it integrates all the advantages of the Potts Model, which is a very rich random partitions model, that we have also modified to propose its Complete Shrinkage version using agglomerative clustering techniques. The model takes also an advantage of Gibbs Fields for its weights precision matrix structure, mainly through Markov Random Fields, and even has five (5) variants structures at the end: the Full-Gibbs, the Sparse-Gibbs, the Between layer Sparse Gibbs which is the B-Sparse Gibbs in a short, the Compound Symmetry Gibbs (CS-Gibbs in short), and the Sparse Compound Symmetry Gibbs (Sparse-CS-Gibbs) model. The Full-Gibbs is mainly to remind fully-connected models, and the other structures are useful to show how the model can be reduced in terms of complexity with sparsity and parsimony. All those models have been experimented with the Mulan project multivariate regression dataset, and the results arouse interest in those structures, in a sense that different structures help to reach different results in terms of Mean Squared Error (MSE) and Relative Root Mean Squared Error (RRMSE). For the Shallow Gibbs Network model, we have found the perfect learning framework : it is the $(l_1, \boldsymbol{\zeta}, \epsilon_{dbs})-\textbf{DBS}$ configuration, which is a combination of the \emph{Universal Approximation Theorem}, and the DBS optimization, coupled with the (\emph{dist})-Nearest Neighbor-(h)-Taylor Series-Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model [which in turn is a combination of the research of the Nearest Neighborhood for a good Train-Test association, the Taylor Approximation Theorem, and finally the Multivariate Interpolation Method]. It indicates that, with an appropriate number $l_1$ of neurons on the hidden layer, an optimal number $\zeta$ of DBS updates, an optimal DBS learnnig rate $\epsilon_{dbs}$, an optimal distance \emph{dist}$_{opt}$ in the research of the nearest neighbor in the training dataset for each test data $x_i^{\mbox{test}}$, an optimal order $h_{opt}$ of the Taylor approximation for the Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model once the {\bfseries DBS} has overfitted the training dataset, the train and the test error converge to zero (0).

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Bayesian Neural Networks

Cited by 47 publications

References 0 publications

Developmental Profiles of Eczema, Wheeze, and Rhinitis: Two Population-Based Birth Cohort Studies

Developmental Profiles of Eczema, Wheeze, and Rhinitis: Two Population-Based Birth Cohort Studies

Real Estate Appraisals with Bayesian Approach and Markov Chain Hybrid Monte Carlo Method: An Application to a Central Urban Area of Naples

The Shallow Gibbs Network, Double Backpropagation and Differential Machine learning

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