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author wolffd
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wolffd@0 1 <html>
wolffd@0 2 <head>
wolffd@0 3 <title>
wolffd@0 4 Netlab Reference Manual gp
wolffd@0 5 </title>
wolffd@0 6 </head>
wolffd@0 7 <body>
wolffd@0 8 <H1> gp
wolffd@0 9 </H1>
wolffd@0 10 <h2>
wolffd@0 11 Purpose
wolffd@0 12 </h2>
wolffd@0 13 Create a Gaussian Process.
wolffd@0 14
wolffd@0 15 <p><h2>
wolffd@0 16 Synopsis
wolffd@0 17 </h2>
wolffd@0 18 <PRE>
wolffd@0 19 net = gp(nin, covarfn)
wolffd@0 20 net = gp(nin, covarfn, prior)
wolffd@0 21 </PRE>
wolffd@0 22
wolffd@0 23
wolffd@0 24 <p><h2>
wolffd@0 25 Description
wolffd@0 26 </h2>
wolffd@0 27
wolffd@0 28 <p><CODE>net = gp(nin, covarfn)</CODE> takes the number of inputs <CODE>nin</CODE>
wolffd@0 29 for a Gaussian Process model with a single output, together
wolffd@0 30 with a string <CODE>covarfn</CODE> which specifies the type of the covariance function,
wolffd@0 31 and returns a data structure <CODE>net</CODE>. The parameters are set to zero.
wolffd@0 32
wolffd@0 33 <p>The fields in <CODE>net</CODE> are
wolffd@0 34 <PRE>
wolffd@0 35 type = 'gp'
wolffd@0 36 nin = number of inputs
wolffd@0 37 nout = number of outputs: always 1
wolffd@0 38 nwts = total number of weights and covariance function parameters
wolffd@0 39 bias = logarithm of constant offset in covariance function
wolffd@0 40 noise = logarithm of output noise variance
wolffd@0 41 inweights = logarithm of inverse length scale for each input
wolffd@0 42 covarfn = string describing the covariance function:
wolffd@0 43 'sqexp'
wolffd@0 44 'ratquad'
wolffd@0 45 fpar = covariance function specific parameters (1 for squared exponential,
wolffd@0 46 2 for rational quadratic)
wolffd@0 47 trin = training input data (initially empty)
wolffd@0 48 trtargets = training target data (initially empty)
wolffd@0 49 </PRE>
wolffd@0 50
wolffd@0 51
wolffd@0 52 <p><CODE>net = gp(nin, covarfn, prior)</CODE> sets a Gaussian prior on the
wolffd@0 53 parameters of the model. <CODE>prior</CODE> must contain the fields
wolffd@0 54 <CODE>pr_mean</CODE> and <CODE>pr_variance</CODE>. If <CODE>pr_mean</CODE> is a scalar,
wolffd@0 55 then the Gaussian is assumed to be isotropic and the additional fields
wolffd@0 56 <CODE>net.pr_mean</CODE> and <CODE>pr_variance</CODE> are set. Otherwise,
wolffd@0 57 the Gaussian prior has a mean
wolffd@0 58 defined by a column vector of parameters <CODE>prior.pr_mean</CODE> and
wolffd@0 59 covariance defined by a column vector of parameters <CODE>prior.pr_variance</CODE>.
wolffd@0 60 Each element of <CODE>prmean</CODE> corresponds to a separate group of parameters, which
wolffd@0 61 need not be mutually exclusive. The membership of the groups is defined
wolffd@0 62 by the matrix <CODE>prior.index</CODE> in which the columns correspond to the elements of
wolffd@0 63 <CODE>prmean</CODE>. Each column has one element for each weight in the matrix,
wolffd@0 64 in the order defined by the function <CODE>gppak</CODE>, and each element
wolffd@0 65 is 1 or 0 according to whether the parameter is a member of the
wolffd@0 66 corresponding group or not. The additional field <CODE>net.index</CODE> is set
wolffd@0 67 in this case.
wolffd@0 68
wolffd@0 69 <p><h2>
wolffd@0 70 See Also
wolffd@0 71 </h2>
wolffd@0 72 <CODE><a href="gppak.htm">gppak</a></CODE>, <CODE><a href="gpunpak.htm">gpunpak</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpcovar.htm">gpcovar</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr>
wolffd@0 73 <b>Pages:</b>
wolffd@0 74 <a href="index.htm">Index</a>
wolffd@0 75 <hr>
wolffd@0 76 <p>Copyright (c) Ian T Nabney (1996-9)
wolffd@0 77
wolffd@0 78
wolffd@0 79 </body>
wolffd@0 80 </html>