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author Daniel Wolff
date Fri, 19 Aug 2016 13:07:06 +0200
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Daniel@0 1 <html>
Daniel@0 2 <head>
Daniel@0 3 <title>
Daniel@0 4 Netlab Reference Manual rbfhess
Daniel@0 5 </title>
Daniel@0 6 </head>
Daniel@0 7 <body>
Daniel@0 8 <H1> rbfhess
Daniel@0 9 </H1>
Daniel@0 10 <h2>
Daniel@0 11 Purpose
Daniel@0 12 </h2>
Daniel@0 13 Evaluate the Hessian matrix for RBF network.
Daniel@0 14
Daniel@0 15 <p><h2>
Daniel@0 16 Synopsis
Daniel@0 17 </h2>
Daniel@0 18 <PRE>
Daniel@0 19 h = rbfhess(net, x, t)
Daniel@0 20 [h, hdata] = rbfhess(net, x, t)
Daniel@0 21 h = rbfhess(net, x, t, hdata)
Daniel@0 22 </PRE>
Daniel@0 23
Daniel@0 24
Daniel@0 25 <p><h2>
Daniel@0 26 Description
Daniel@0 27 </h2>
Daniel@0 28 <CODE>h = rbfhess(net, x, t)</CODE> takes an RBF network data structure <CODE>net</CODE>,
Daniel@0 29 a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of target
Daniel@0 30 values and returns the full Hessian matrix <CODE>h</CODE> corresponding to
Daniel@0 31 the second derivatives of the negative log posterior distribution,
Daniel@0 32 evaluated for the current weight and bias values as defined by
Daniel@0 33 <CODE>net</CODE>. Currently, the implementation only computes the
Daniel@0 34 Hessian for the output layer weights.
Daniel@0 35
Daniel@0 36 <p><CODE>[h, hdata] = rbfhess(net, x, t)</CODE> returns both the Hessian matrix
Daniel@0 37 <CODE>h</CODE> and the contribution <CODE>hdata</CODE> arising from the data dependent
Daniel@0 38 term in the Hessian.
Daniel@0 39
Daniel@0 40 <p><CODE>h = rbfhess(net, x, t, hdata)</CODE> takes a network data structure
Daniel@0 41 <CODE>net</CODE>, a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of
Daniel@0 42 target values, together with the contribution <CODE>hdata</CODE> arising from
Daniel@0 43 the data dependent term in the Hessian, and returns the full Hessian
Daniel@0 44 matrix <CODE>h</CODE> corresponding to the second derivatives of the negative
Daniel@0 45 log posterior distribution. This version saves computation time if
Daniel@0 46 <CODE>hdata</CODE> has already been evaluated for the current weight and bias
Daniel@0 47 values.
Daniel@0 48
Daniel@0 49 <p><h2>
Daniel@0 50 Example
Daniel@0 51 </h2>
Daniel@0 52 For the standard regression framework with a Gaussian conditional
Daniel@0 53 distribution of target values given input values, and a simple
Daniel@0 54 Gaussian prior over weights, the Hessian takes the form
Daniel@0 55 <PRE>
Daniel@0 56
Daniel@0 57 h = beta*hdata + alpha*I
Daniel@0 58 </PRE>
Daniel@0 59
Daniel@0 60
Daniel@0 61 <p><h2>
Daniel@0 62 See Also
Daniel@0 63 </h2>
Daniel@0 64 <CODE><a href="mlphess.htm">mlphess</a></CODE>, <CODE><a href="hesschek.htm">hesschek</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE><hr>
Daniel@0 65 <b>Pages:</b>
Daniel@0 66 <a href="index.htm">Index</a>
Daniel@0 67 <hr>
Daniel@0 68 <p>Copyright (c) Ian T Nabney (1996-9)
Daniel@0 69
Daniel@0 70
Daniel@0 71 </body>
Daniel@0 72 </html>