📄 glmhess.htm
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<html><head><title>Netlab Reference Manual glmhess</title></head><body><H1> glmhess</H1><h2>Purpose</h2>Evaluate the Hessian matrix for a generalised linear model.<p><h2>Synopsis</h2><PRE>h = glmhess(net, x, t)[h, hdata] = glmhess(net, x, t)h = glmhess(net, x, t, hdata)</PRE><p><h2>Description</h2><CODE>h = glmhess(net, x, t)</CODE> takes a GLM network data structure <CODE>net</CODE>, a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of targetvalues and returns the full Hessian matrix <CODE>h</CODE> corresponding tothe second derivatives of the negative log posterior distribution,evaluated for the current weight and bias values as defined by<CODE>net</CODE>. Note that the target data is not required in the calculation,but is included to make the interface uniform with <CODE>nethess</CODE>. Forlinear and logistic outputs, the computation is very simple and is done (in effect) in one line in <CODE>glmtrain</CODE>.<p><CODE>[h, hdata] = glmhess(net, x, t)</CODE> returns both the Hessian matrix<CODE>h</CODE> and the contribution <CODE>hdata</CODE> arising from the data dependentterm in the Hessian.<p><CODE>h = glmhess(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 fromthe data dependent term in the Hessian, and returns the full Hessianmatrix <CODE>h</CODE> corresponding to the second derivatives of the negativelog posterior distribution. This version saves computation time if<CODE>hdata</CODE> has already been evaluated for the current weight and biasvalues.<p><h2>Example</h2>The Hessian matrix is used by <CODE>glmtrain</CODE> to take a Newton step forsoftmax outputs.<PRE>Hessian = glmhess(net, x, t);deltaw = -gradient*pinv(Hessian);</PRE><p><h2>See Also</h2><CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE>, <CODE><a href="hesschek.htm">hesschek</a></CODE>, <CODE><a href="nethess.htm">nethess</a></CODE><hr><b>Pages:</b><a href="index.htm">Index</a><hr><p>Copyright (c) Ian T Nabney (1996-9)</body></html>⌨️ 快捷键说明
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