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nns_buildbayes

building of a neural network with 1 hidden layer and with bias

Calling sequence

[result]=nns_buildbayes(wh_in,wo_in,x,y, (options))

Arguments

wh_in:

coefficients of the hidden neurons + bias, obtained from the initialization step

wh_in is a matrix of dimensions ((q+1) x nh) or a Div structure

nh is the number of hidden neurons

wo_in:

coefficients of the output neurons + bias, obtained from the initialization step

wo_in is a matrix of dimensions ((nh+1) x no) or a Div structure

no is the number of output neurons

x:

calibration dataset

x is a matrix of dimensions (n x q) or a Div structure

y:

reference values, to be predicted

y is a matrix of dimensions (n x no) or a Div structure

(options_in):

options for the building of the model

options_in.maxtime: max. run time, in seconds (default=300)

options_in.maxiter: max. number of iterations (default=10000)

options_in.displayfreq: gap between two successive iterations to be plotted in a figure (default=10)

options_in.precresid: accuracy of the residuals; a scalar or a vector of length no (default=1e-6*stdout)

options_in.precparam: accuracy of the parameters; a scalar or a vector of length nc (default=1e-4)

options_in.stdresmin: minimum of the standard errors of the residuals; a scalar or a vector of length no (default=1e-6*stdout)

options_in.stdresmax: maximum of the standard errors of the residuals; a scalar or a vector of length no (default=0.1*stdout)

options_in.regclass: weights regularization

… 0 = no regularization

… 1 = a class for all weights

… 2 = two classes: one for the inputs, the other for the outputs

… 3 = a class for each input, a class for the bias of the hidden layer and a class for each output (by default)

… 4 = a class for each weight

options_in.preproc: preprocessings before learning

… 0 = no preprocessing

… 1 = normalization (sum of squares of the differences between the inputs and the outputs = n)

… 2 = standardization (inputs mean = outputs mean = 0, sum of squares of the residuals = n)

options_in.momentparam: tuning of the effective number in each class; between 0 and 1 (default = 0.8)

result.wh_out:

coefficients of the hidden neurons + bias, after model calculation

result.wh_out is a matrix of dimension ((q+1) x no) or a Div structure

nh is the number of hidden neurons

result.wo_out:

coefficients of the output neurons + biais, after model calculation

result.wo_out is a matrix of dimensions ((nh + 1) x no) or a Div structure

no is the number of output neurons

result.stdres:

estimation of the standard error of the residuals

result.stdres is a Div structure

result.stdres.d is a vector of dimensions (1 x no)

result.covw:

estimation of the variance-covariance matrix for the weights

result.covw is a Div structure

result.covw.d is a matrix of dimensions (nw x nw)

result.options_out:

options_in with the following fields:

result.options_out.stop: a string message about the learning stop

result.options_out.r2: square correlation coefficient for each output

result.options_out.wheff: ratio number of parameters effective/total for each weight of the hidden layer

result.options_out.wheff.d is a matrix of dimensions ((q+1) x nh)

result.options_out.woeff: ratio number of parameters effective/total for each weight of the output layer

result.options_out.woeff.d is a matrix of dimensions ((nh+1) x no)

result.options_out.histiters: number of iterations

result.options_out.histresid: residual errors for each iteration

result.options_out.histresid.d is a matrix of no lines and as columns as iterations

result.options_out.histparam: effective number of parameters, for each class

result.options_out.histparam.d has as coulons as classes and as lines as iterations

result.options_out.classnumbers: number of class for each weight, ranked in a vector according to [wh(:);wo(:)]

result.options_out.totalparam: total number of parameters (weights) in each class of weights

result.options_out.totalparam.d is a line vector with as columns as classes

Examples

[res]=nns_buildbayes(wh,wo,x,y)

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