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