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