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author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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+++ b/toolboxes/FullBNT-1.0.7/nethelp3.3/mlphess.htm	Tue Feb 10 15:05:51 2015 +0000
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+<html>
+<head>
+<title>
+Netlab Reference Manual mlphess
+</title>
+</head>
+<body>
+<H1> mlphess
+</H1>
+<h2>
+Purpose
+</h2>
+Evaluate the Hessian matrix for a multi-layer perceptron network.
+
+<p><h2>
+Synopsis
+</h2>
+<PRE>
+h = mlphess(net, x, t)
+[h, hdata] = mlphess(net, x, t)
+h = mlphess(net, x, t, hdata)
+</PRE>
+
+
+<p><h2>
+Description
+</h2>
+<CODE>h = mlphess(net, x, t)</CODE> takes an MLP network data structure <CODE>net</CODE>,
+a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of target
+values and returns the full Hessian matrix <CODE>h</CODE> corresponding to
+the second derivatives of the negative log posterior distribution,
+evaluated for the current weight and bias values as defined by
+<CODE>net</CODE>.
+
+<p><CODE>[h, hdata] = mlphess(net, x, t)</CODE> returns both the Hessian matrix
+<CODE>h</CODE> and the contribution <CODE>hdata</CODE> arising from the data dependent
+term in the Hessian.
+
+<p><CODE>h = mlphess(net, x, t, hdata)</CODE> takes a network data structure
+<CODE>net</CODE>, a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of 
+target values, together with the contribution <CODE>hdata</CODE> arising from
+the data dependent term in the Hessian, and returns the full Hessian
+matrix <CODE>h</CODE> corresponding to the second derivatives of the negative
+log posterior distribution. This version saves computation time if
+<CODE>hdata</CODE> has already been evaluated for the current weight and bias
+values.
+
+<p><h2>
+Example
+</h2>
+For the standard regression framework with a Gaussian conditional
+distribution of target values given input values, and a simple
+Gaussian prior over weights, the Hessian takes the form
+<PRE>
+
+    h = beta*hd + alpha*I
+</PRE>
+
+where the contribution <CODE>hd</CODE> is evaluated by calls to <CODE>mlphdotv</CODE> and
+<CODE>h</CODE> is the full Hessian.
+
+<p><h2>
+See Also
+</h2>
+<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>
+<b>Pages:</b>
+<a href="index.htm">Index</a>
+<hr>
+<p>Copyright (c) Ian T Nabney (1996-9)
+
+
+</body>
+</html>
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