function demprgp(action);
%DEMPRGP Demonstrate sampling from a Gaussian Process prior.
%
% Description
% This function plots the functions represented by a Gaussian Process
% model. The hyperparameter values can be adjusted on a linear scale
% using the sliders (though the exponential of the parameters is used
% in the covariance function), or by typing values into the text boxes
% and pressing the return key. Both types of covariance function are
% supported. An extra function specific parameter is needed for the
% rational quadratic function.
%
% See also
% GP
%
% Copyright (c) Ian T Nabney (1996-2001)
if nargin<1,
action='initialize';
end;
if strcmp(action,'initialize')
% Bounds on hyperparameter values
biasminval = -3.0; biasmaxval = 3.0;
noiseminval = -20; noisemaxval = -2;
fparminval = 0.0; fparmaxval = 2.0;
inwminval = 0; inwmaxval = 8;
% Initial hyperparameter values
bias = (biasminval+biasmaxval)/2;
noise = (noiseminval+noisemaxval)/2;
inweights = (inwminval+inwmaxval)/2;
fpar = (fparminval+fparmaxval)/2;
fpar2 = (fparminval+fparmaxval)/2;
gptype = 'sqexp';
% Create FIGURE
fig=figure( ...
'Name','Sampling from a Gaussian Process prior', ...
'Position', [50 50 480 380], ...
'NumberTitle','off', ...
'Color', [0.8 0.8 0.8], ...
'Visible','on');
% List box for covariance function type
nettype_box = uicontrol(fig, ...
'Style', 'listbox', ...
'Units', 'normalized', ...
'HorizontalAlignment', 'center', ...
'Position', [0.52 0.77 0.40 0.12], ...
'String', 'Squared Exponential|Rational Quadratic', ...
'Max', 1, 'Min', 0, ... % Only allow one selection
'Value', 1, ... % Initial value is squared exponential
'BackgroundColor',[0.60 0.60 0.60],...
'CallBack', 'demprgp GPtype');
% Title for list box
uicontrol(fig, ...
'Style', 'text', ...
'Units', 'normalized', ...
'Position', [0.52 0.89 0.40 0.05], ...
'String', 'Covariance Function Type', ...
'BackgroundColor', get(fig, 'Color'), ...
'HorizontalAlignment', 'center');
% Frames to enclose sliders
bottom_row = 0.04;
slider_frame_height = 0.15;
biasframe = uicontrol(fig, ...
'Style', 'frame', ...
'Units', 'normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'String', 'bias', ...
'HorizontalAlignment', 'left', ...
'Position', [0.05 bottom_row 0.35 slider_frame_height]);
bpos = get(biasframe, 'Position');
noise_frame_bottom = bpos(2) + bpos(4) + 0.02;
noiseframe = uicontrol(fig, ...
'Style', 'frame', ...
'Units', 'normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.05 noise_frame_bottom 0.35 slider_frame_height]);
npos = get(noiseframe, 'Position');
inw_frame_bottom = npos(2) + npos(4) + 0.02;
inwframe = uicontrol(fig, ...
'Style', 'frame', ...
'Units', 'normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.05 inw_frame_bottom 0.35 slider_frame_height]);
inwpos = get(inwframe, 'Position');
fpar_frame_bottom = inwpos(2) + inwpos(4) + 0.02;
% This frame sometimes has multiple parameters
uicontrol(fig, ...
'Style', 'frame', ...
'Units', 'normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.05 fpar_frame_bottom 0.35 2*slider_frame_height]);
% Frame text
slider_text_height = 0.05;
slider_text_voffset = 0.08;
uicontrol(fig, ...
'Style', 'text', ...
'Units', 'normalized', ...
'HorizontalAlignment', 'left', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.07 bottom_row+slider_text_voffset ...
0.06 slider_text_height], ...
'String', 'bias');
% Frame text
noiseframe = uicontrol(fig, ...
'Style', 'text', ...
'Units', 'normalized', ...
'HorizontalAlignment', 'left', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.07 noise_frame_bottom+slider_text_voffset ...
0.08 slider_text_height], ...
'String', 'noise');
% Frame text
uicontrol(fig, ...
'Style', 'text', ...
'Units', 'normalized', ...
'HorizontalAlignment', 'left', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.07 inw_frame_bottom+slider_text_voffset ...
0.14 slider_text_height], ...
'String', 'inweights');
% Frame text
uicontrol(fig, ...
'Style', 'text', ...
'Units', 'normalized', ...
'HorizontalAlignment', 'left', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.07 fpar_frame_bottom+slider_frame_height+ ...
slider_text_voffset 0.06 slider_text_height], ...
'String', 'fpar');
uicontrol(fig, ...
'Style', 'text', ...
'Units', 'normalized', ...
'HorizontalAlignment', 'left', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.07 fpar_frame_bottom+slider_text_voffset ...
0.06 slider_text_height], ...
'String', 'fpar2', ...
'Tag', 'fpar2text', ...
'Enable', 'off');
% Slider
slider_left = 0.07;
slider_width = 0.31;
slider_frame_voffset = 0.02;
biasslide = uicontrol(fig, ...
'Style', 'slider', ...
'Units', 'normalized', ...
'Value', bias, ...
'BackgroundColor', [0.8 0.8 0.8], ...
'Position', [slider_left bottom_row+slider_frame_voffset ...
slider_width 0.05], ...
'Min', biasminval, 'Max', biasmaxval, ...
'Callback', 'demprgp update');
% Slider
noiseslide = uicontrol(fig, ...
'Style', 'slider', ...
'Units', 'normalized', ...
'Value', noise, ...
'BackgroundColor', [0.8 0.8 0.8], ...
'Position', [slider_left noise_frame_bottom+slider_frame_voffset ...
slider_width 0.05], ...
'Min', noiseminval, 'Max', noisemaxval, ...
'Callback', 'demprgp update');
% Slider
inweightsslide = uicontrol(fig, ...
'Style', 'slider', ...
'Units', 'normalized', ...
'Value', inweights, ...
'BackgroundColor', [0.8 0.8 0.8], ...
'Position', [slider_left inw_frame_bottom+slider_frame_voffset ...
slider_width 0.05], ...
'Min', inwminval, 'Max', inwmaxval, ...
'Callback', 'demprgp update');
% Slider
fparslide = uicontrol(fig, ...
'Style', 'slider', ...
'Units', 'normalized', ...
'Value', fpar, ...
'BackgroundColor', [0.8 0.8 0.8], ...
'Position', [slider_left fpar_frame_bottom+slider_frame_height+ ...
slider_frame_voffset slider_width 0.05], ...
'Min', fparminval, 'Max', fparmaxval, ...
'Callback', 'demprgp update');
fpar2slide = uicontrol(fig, ...
'Style', 'slider', ...
'Units', 'normalized', ...
'Value', fpar2, ...
'BackgroundColor', [0.8 0.8 0.8], ...
'Position', [slider_left fpar_frame_bottom+slider_frame_voffset ...
slider_width 0.05], ...
'Min', fparminval, 'Max', fparmaxval, ...
'Callback', 'demprgp update', ...
'Tag', 'fpar2slider', ...
'Enable', 'off');
% Text display of hyper-parameter values
format = '%8f';
hp_left = 0.20;
hp_width = 0.17;
biasval = uicontrol(fig, ...
'Style', 'edit', ...
'Units', 'normalized', ...
'Position', [hp_left bottom_row+slider_text_voffset ...
hp_width slider_text_height], ...
'String', sprintf(format, bias), ...
'Callback', 'demprgp newval');
noiseval = uicontrol(fig, ...
'Style', 'edit', ...
'Units', 'normalized', ...
'Position', [hp_left noise_frame_bottom+slider_text_voffset ...
hp_width slider_text_height], ...
'String', sprintf(format, noise), ...
'Callback', 'demprgp newval');
inweightsval = uicontrol(fig, ...
'Style', 'edit', ...
'Units', 'normalized', ...
'Position', [hp_left inw_frame_bottom+slider_text_voffset ...
hp_width slider_text_height], ...
'String', sprintf(format, inweights), ...
'Callback', 'demprgp newval');
fparval = uicontrol(fig, ...
'Style', 'edit', ...
'Units', 'normalized', ...
'Position', [hp_left fpar_frame_bottom+slider_frame_height+ ...
slider_text_voffset hp_width slider_text_height], ...
'String', sprintf(format, fpar), ...
'Callback', 'demprgp newval');
fpar2val = uicontrol(fig, ...
'Style', 'edit', ...
'Units', 'normalized', ...
'Position', [hp_left fpar_frame_bottom+slider_text_voffset ...
hp_width slider_text_height], ...
'String', sprintf(format, fpar), ...
'Callback', 'demprgp newval', ...
'Enable', 'off', ...
'Tag', 'fpar2val');
% The graph box
haxes = axes('Position', [0.5 0.28 0.45 0.45], ...
'Units', 'normalized', ...
'Visible', 'on');
% The SAMPLE button
uicontrol(fig, ...
'Style','push', ...
'Units','normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position',[0.5 bottom_row 0.13 0.1], ...
'String','Sample', ...
'Callback','demprgp replot');
% The CLOSE button
uicontrol(fig, ...
'Style','push', ...
'Units','normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position',[0.82 bottom_row 0.13 0.1], ...
'String','Close', ...
'Callback','close(gcf)');
% The HELP button
uicontrol(fig, ...
'Style','push', ...
'Units','normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position',[0.66 bottom_row 0.13 0.1], ...
'String','Help', ...
'Callback','demprgp help');
% Save handles to objects
hndlList=[fig biasslide noiseslide inweightsslide fparslide ...
biasval noiseval inweightsval ...
fparval haxes nettype_box];
set(fig, 'UserData', hndlList);
demprgp('replot')
elseif strcmp(action, 'update'),
% Update when a slider is moved.
hndlList = get(gcf, 'UserData');
biasslide = hndlList(2);
noiseslide = hndlList(3);
inweightsslide = hndlList(4);
fparslide = hndlList(5);
biasval = hndlList(6);
noiseval = hndlList(7);
inweightsval = hndlList(8);
fparval = hndlList(9);
haxes = hndlList(10);
nettype_box = hndlList(11);
bias = get(biasslide, 'Value');
noise = get(noiseslide, 'Value');
inweights = get(inweightsslide, 'Value');
fpar = get(fparslide, 'Value');
fpar2 = get(findobj('Tag', 'fpar2slider'), 'Value');
format = '%8f';
set(biasval, 'String', sprintf(format, bias));
set(noiseval, 'String', sprintf(format, noise));
set(inweightsval, 'String', sprintf(format, inweights));
set(fparval, 'String', sprintf(format, fpar));
set(findobj('Tag', 'fpar2val'), 'String', ...
sprintf(format, fpar2));
demprgp('replot');
elseif strcmp(action, 'newval'),
% Update when text is changed.
hndlList = get(gcf, 'UserData');
biasslide = hndlList(2);
noiseslide = hndlList(3);
inweightsslide = hndlList(4);
fparslide = hndlList(5);
biasval = hndlList(6);
noiseval = hndlList(7);
inweightsval = hndlList(8);
fparval = hndlList(9);
haxes = hndlList(10);
bias = sscanf(get(biasval, 'String'), '%f');
noise = sscanf(get(noiseval, 'String'), '%f');
inweights = sscanf(get(inweightsval, 'String'), '%f');
fpar = sscanf(get(fparval, 'String'), '%f');
fpar2 = sscanf(get(findobj('Tag', 'fpar2val'), 'String'), '%f');
set(biasslide, 'Value', bias);
set(noiseslide, 'Value', noise);
set(inweightsslide, 'Value', inweights);
set(fparslide, 'Value', fpar);
set(findobj('Tag', 'fpar2slider'), 'Value', fpar2);
demprgp('replot');
elseif strcmp(action, 'GPtype')
hndlList = get(gcf, 'UserData');
nettype_box = hndlList(11);
gptval = get(nettype_box, 'Value');
if gptval == 1
% Squared exponential, so turn off fpar2
set(findobj('Tag', 'fpar2text'), 'Enable', 'off');
set(findobj('Tag', 'fpar2slider'), 'Enable', 'off');
set(findobj('Tag', 'fpar2val'), 'Enable', 'off');
else
% Rational quadratic, so turn on fpar2
set(findobj('Tag', 'fpar2text'), 'Enable', 'on');
set(findobj('Tag', 'fpar2slider'), 'Enable', 'on');
set(findobj('Tag', 'fpar2val'), 'Enable', 'on');
end
demprgp('replot');
elseif strcmp(action, 'replot'),
% Re-sample from the prior and plot graphs.
oldFigNumber=watchon;
hndlList = get(gcf, 'UserData');
biasslide = hndlList(2);
noiseslide = hndlList(3);
inweightsslide = hndlList(4);
fparslide = hndlList(5);
haxes = hndlList(10);
nettype_box = hndlList(11);
gptval = get(nettype_box, 'Value');
if gptval == 1
gptype = 'sqexp';
else
gptype = 'ratquad';
end
bias = get(biasslide, 'Value');
noise = get(noiseslide, 'Value');
inweights = get(inweightsslide, 'Value');
fpar = get(fparslide, 'Value');
axes(haxes);
cla
set(gca, ...
'Box', 'on', ...
'Color', [0 0 0], ...
'XColor', [0 0 0], ...
'YColor', [0 0 0], ...
'FontSize', 14);
ymin = -10;
ymax = 10;
axis([-1 1 ymin ymax]);
set(gca,'DefaultLineLineWidth', 2);
xvals = (-1:0.01:1)';
nsample = 10; % Number of samples from prior.
hold on
plot([-1 0; 1 0], [0 ymin; 0 ymax], 'b--');
net = gp(1, gptype);
net.bias = bias;
net.noise = noise;
net.inweights = inweights;
if strcmp(gptype, 'sqexp')
net.fpar = fpar;
else
fpar2 = get(findobj('Tag', 'fpar2slider'), 'Value');
net.fpar = [fpar fpar2];
end
cn = gpcovar(net, xvals);
cninv = inv(cn);
cnchol = chol(cn);
set(gca, 'DefaultLineLineWidth', 1);
for n = 1:nsample
y = (cnchol') * randn(size(xvals));
plot(xvals, y, 'y');
end
watchoff(oldFigNumber);
elseif strcmp(action, 'help'),
% Provide help to user.
oldFigNumber=watchon;
helpfig = figure('Position', [100 100 480 400], ...
'Name', 'Help', ...
'NumberTitle', 'off', ...
'Color', [0.8 0.8 0.8], ...
'Visible','on');
% The HELP TITLE BAR frame
uicontrol(helpfig, ...
'Style','frame', ...
'Units','normalized', ...
'HorizontalAlignment', 'center', ...
'Position', [0.05 0.82 0.9 0.1], ...
'BackgroundColor',[0.60 0.60 0.60]);
% The HELP TITLE BAR text
uicontrol(helpfig, ...
'Style', 'text', ...
'Units', 'normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position', [0.26 0.85 0.6 0.05], ...
'HorizontalAlignment', 'left', ...
'String', 'Help: Sampling from a Gaussian Process Prior');
helpstr1 = strcat(...
'This demonstration shows the effects of sampling from a Gaussian', ...
' process prior. The parameters bias, noise, inweights and fpar', ...
' control the corresponding terms in the covariance function of the',...
' Gaussian process. Their values can be adjusted on a linear scale',...
' using the sliders, or by typing values into the text boxes and',...
' pressing the return key. After setting these values, press the',...
' ''Sample'' button to see a new sample from the prior.');
helpstr2 = strcat(...
'Observe how inweights controls horizontal length-scale of the',...
' variation in the functions, noise controls the roughness of the',...
' functions, and the bias controls the size of the', ...
' vertical offset of the signal.');
helpstr3 = strcat(...
'There are two types of covariance function supported by', ...
' Netlab which can be selected using the ''Covariance Function', ...
' Type'' menu.');
helpstr4 = strcat(...
'The squared exponential has a single fpar which', ...
' controls the vertical scale of the process.');
helpstr5 = strcat(...
'The rational quadratic has two fpar values. The first is', ...
' is a scale parameter inside the rational function like the',...
' first fpar for the squared exponential covariance, while the', ...
' second gives the exponent of the rational function (i.e. the',...
' rate of decay of the covariance function.');
% Set up cell array with help strings
hstr(1) = {helpstr1};
hstr(2) = {''};
hstr(3) = {helpstr2};
hstr(4) = {''};
hstr(5) = {helpstr3};
hstr(6) = {''};
hstr(7) = {helpstr4};
hstr(8) = {''};
hstr(9) = {helpstr5};
% The HELP text
helpui = uicontrol(helpfig, ...
'Style', 'Text', ...
'Units', 'normalized', ...
'ForegroundColor', [0 0 0], ...
'HorizontalAlignment', 'left', ...
'BackgroundColor', [1 1 1], ...
'Min', 0, ...
'Max', 2, ...
'Position', [0.05 0.2 0.9 0.57]);
[hstrw, newpos] = textwrap(helpui, hstr);
set(helpui, 'String', hstrw, 'Position', [0.05, 0.2, 0.9 newpos(4)]);
% The CLOSE button
uicontrol(helpfig, ...
'Style','push', ...
'Units','normalized', ...
'BackgroundColor', [0.6 0.6 0.6], ...
'Position',[0.4 0.05 0.2 0.1], ...
'String','Close', ...
'Callback','close(gcf)');
watchoff(oldFigNumber);
end;
