%?Calculates?for?xstar?x-coordinates?the?bestEstimate?and?the?95%
%?confidence?interval?（bounds）?for?a?Gaussian?process?regression.
%?Mark?Ebden?July?2008
%
%?Inputs:
%??k?-?a?handle?to?the?covariance?function
%??Xy?-?the?training?data?x-?and?y-coordinates
%??theta?-?the?GP?parameters?to?be?passed?to?the?covariance?function
%??????????（e.g.?length?scale?periodicity?etc.
%??sigma_n?-?the?noise?（optional?--?default?0）
%????NOTE:?sigma_n?should?be?left?as?zero?if?k?*already*?includes?the?noise?term?as?I?usually?do.
%??xstar?-?specify?the?x-coordinates?to?solve?for?（optional?--?default?is
%??????????to?let?the?algorithm?choose?them）
%??graphing?-?produce?a?plot?of?results?（optional）
%?????????????Default?is?to?plot?the?results?unless?the?function?outputs?were?asked?for
%
%?Outputs:
%??xstar?-?x-coordinates?（default?100?are?chosen）
%??K?-?covariance?matrix?among?training?data
%??V?-?variance?at?each?xstar

function?[xstar?bestEstimate?bounds?K?V]?=?calcGP?（k?X?y?theta?sigma_n?xstar?graphing）

if?nargin?????if?nargout?==?0
????????graphing?=?1;?
????else
????????graphing?=?0;
????end
end
if?nargin?????r2?=（max（X）-min（X））;
????N?=?1e3;?%?How?many?points?to?use
????z?=?.5;?%?How?much?to?extend?the?time?series?on?either?side?（e.g.?.5?is?50%?extension?on?left?and?on?right）
????xstar?=?（0:N）/N?*?（z*2+1）*r2?+?min（X）-r2*z;
end
if?nargin?????sigma_n?=?0;
end
if?nargin?????theta?=?[1?0?1?0];
end

%?a）?Initializations
meany?=?mean（y）;?y?=?y?-?meany;
n?=?size（X1）;?lx?=?length（xstar）;
K?=?zeros（n）;?kstar?=?zeros（n1）;
for?i?=?1:n
????for?j?=?1:n
????????K（ij）?=?k?（X（i）X（j）theta）;
????end
end
fstarbar?=?zeros（lx1）;?V?=?zeros（lx1）;

%?b）?One-off?calculations
diags?=?max（1e3*eps?sigma_n^2）;?%?beef?up?the?diagonal?if?sigma_n?=?0
L?=?chol?（K?+?diags*eye（n）‘lower‘）;?
alpha?=?L‘\（L\y）;
logpyX?=?-y‘*alpha/2?-?sum（log（diag（L）））?-?n*log（2*pi）/2;?%?Log?marginal?likelihood

%?c）?xstar?loop
for?q?=?1:lx
????for?i?=?1:n
????????kstar（i）?=?k?（X（i）xstar（q）theta）;
????end
????kstar
????%?Mean?of?prediction
????fstarbar（q）?=?kstar‘?*?alpha;
????%?Variance?of?prediction
????v?=?L\kstar;
????ystar_noise?=?sigma_n^2;?%?recall?f*?has?no?noise?itself?（Algorithm?2.1?on?p?19?of?H152）
????V（q）?=?k?（xstar（q）xstar（q）theta）?-?v‘*v?+?ystar_noise;
end
bounds?=?[fstarbar+1.96*sqrt（V）?fstarbar-1.96*sqrt（V）]+meany;
bestEstimate?=?fstarbar+meany;

%?d）?Output
if?graphing?==?1
????figure?hold?on
????stdRegion?（xstarbounds）
????plot?（xstarbestEstimate‘k‘）
????plot?（Xy+meany‘b+‘）
end

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件??????31996??2006-03-07?20:29??gpml\doc\alg21.gif

?????文件??????43172??2006-03-07?20:08??gpml\doc\alg31.gif

?????文件??????34064??2006-03-07?20:08??gpml\doc\alg32.gif

?????文件??????66673??2006-03-07?20:08??gpml\doc\alg35.gif

?????文件??????32226??2006-03-07?20:08??gpml\doc\alg36.gif

?????文件??????60084??2006-03-07?20:08??gpml\doc\alg51.gif

?????文件??????41085??2006-03-07?20:08??gpml\doc\alg52.gif

?????文件??????34439??2006-03-26?03:00??gpml\doc\classification.html

?????文件??????36772??2006-03-15?00:12??gpml\doc\fig2d.gif

?????文件??????35364??2006-03-15?00:12??gpml\doc\fig2de1.gif

?????文件??????42683??2006-03-15?00:12??gpml\doc\fig2de2.gif

?????文件??????38483??2006-03-15?00:12??gpml\doc\fig2de3.gif

?????文件??????34059??2006-03-15?00:12??gpml\doc\fig2dl1.gif

?????文件??????40431??2006-03-15?00:12??gpml\doc\fig2dl2.gif

?????文件??????38375??2006-03-15?00:12??gpml\doc\fig2dl3.gif

?????文件??????17875??2006-03-10?22:56??gpml\doc\figepp.gif

?????文件??????23299??2006-03-10?22:56??gpml\doc\figepp2.gif

?????文件???????6109??2006-03-27?15:58??gpml\doc\figl.gif

?????文件??????21386??2006-03-07?20:29??gpml\doc\figl1.gif

?????文件??????17854??2006-03-09?23:57??gpml\doc\figlapp.gif

?????文件??????25557??2006-03-09?23:57??gpml\doc\figlapp2.gif

?????文件??????16078??2006-03-27?16:35??gpml\doc\figlf.gif

?????文件??????16712??2006-03-27?22:10??gpml\doc\figlm.gif

?????文件???????3461??2007-06-26?18:30??gpml\doc\index.html

?????文件??????16598??2006-03-29?01:45??gpml\doc\regression.html

?????文件???????7738??2006-03-29?18:39??gpml\doc\sparse-approx.html

?????文件?????????77??2006-03-07?20:08??gpml\doc\style.css

?????文件???????5097??2007-07-24?23:34??gpml\gpml\approxEP.m

?????文件???????1936??2007-06-27?19:45??gpml\gpml\approximations.m

?????文件???????3094??2007-06-26?18:12??gpml\gpml\approxLA.m

............此處省略60個文件信息