Daniel@0: Daniel@0: Daniel@0: Daniel@0: Netlab Reference Manual mlphess Daniel@0: Daniel@0: Daniel@0: Daniel@0:

mlphess Daniel@0:

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Daniel@0: Purpose Daniel@0:

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

Daniel@0: Synopsis Daniel@0:

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

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

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

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

Daniel@0: Example Daniel@0:

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

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

Daniel@0: See Also Daniel@0:

Daniel@0: mlp, hesschek, mlphdotv, evidence

Daniel@0: Pages: Daniel@0: Index Daniel@0:

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