wolffd@0: wolffd@0: wolffd@0: wolffd@0: Netlab Reference Manual mlphess wolffd@0: wolffd@0: wolffd@0: wolffd@0:

mlphess wolffd@0:

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wolffd@0: Purpose wolffd@0:

wolffd@0: Evaluate the Hessian matrix for a multi-layer perceptron network. wolffd@0: wolffd@0:

wolffd@0: Synopsis wolffd@0:

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wolffd@0: h = mlphess(net, x, t)
wolffd@0: [h, hdata] = mlphess(net, x, t)
wolffd@0: h = mlphess(net, x, t, hdata)
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wolffd@0: wolffd@0: wolffd@0:

wolffd@0: Description wolffd@0:

wolffd@0: h = mlphess(net, x, t) takes an MLP network data structure net, wolffd@0: a matrix x of input values, and a matrix t of target wolffd@0: values and returns the full Hessian matrix h corresponding to wolffd@0: the second derivatives of the negative log posterior distribution, wolffd@0: evaluated for the current weight and bias values as defined by wolffd@0: net. wolffd@0: wolffd@0:

[h, hdata] = mlphess(net, x, t) returns both the Hessian matrix wolffd@0: h and the contribution hdata arising from the data dependent wolffd@0: term in the Hessian. wolffd@0: wolffd@0:

h = mlphess(net, x, t, hdata) takes a network data structure wolffd@0: net, a matrix x of input values, and a matrix t of wolffd@0: target values, together with the contribution hdata arising from wolffd@0: the data dependent term in the Hessian, and returns the full Hessian wolffd@0: matrix h corresponding to the second derivatives of the negative wolffd@0: log posterior distribution. This version saves computation time if wolffd@0: hdata has already been evaluated for the current weight and bias wolffd@0: values. wolffd@0: wolffd@0:

wolffd@0: Example wolffd@0:

wolffd@0: For the standard regression framework with a Gaussian conditional wolffd@0: distribution of target values given input values, and a simple wolffd@0: Gaussian prior over weights, the Hessian takes the form wolffd@0:

wolffd@0: 
wolffd@0:     h = beta*hd + alpha*I
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wolffd@0: wolffd@0: where the contribution hd is evaluated by calls to mlphdotv and wolffd@0: h is the full Hessian. wolffd@0: wolffd@0:

wolffd@0: See Also wolffd@0:

wolffd@0: mlp, hesschek, mlphdotv, evidence

wolffd@0: Pages: wolffd@0: Index wolffd@0:

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