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