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regressmulti_fitfun.m
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regressmulti_fitfun.m
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function [fitness,gp,theta,ypredtrain,fitnessTest,ypredtest,pvals,r2train,r2test,r2val,geneOutputs,geneOutputsTest,geneOutputsVal]=regressmulti_fitfun(evalstr,gp)
%REGRESSMULTI_FITFUN Fitness function for multigene symbolic regression.
%
% This is the default fitness function for multigene symbolic regression
% in GPTIPS.
%
% [FITNESS,GP] = REGRESSMULTI_FITFUN(EVALSTR,GP) returns the FITNESS of
% the symbolic expression(s) in the cell array EVALSTR using information
% contained in the GP data struct. Here, FITNESS is the root mean squared
% prediction error (RMSE) on the training data set.
%
% [FITNESS,GP,THETA,YPREDTRAIN,FITNESS_TEST,YPREDTEST,PVALS,R2TRAIN,R2TEST,R2VAL]
% = REGRESSMULTI_FITFUN(EVALSTR,GP) may be used post-run to return the
% gene coefficients THETA, the prediction of the model on the training
% data YPREDTRAIN, the RMSE fitness value FITNESS_TEST on the test data
% set, the prediction of the model on the test data YPREDTEST, the
% statistical p-values for bias and model terms are returned as PVALS
% (PVALS only computed if the Statistics Toolbox is present, otherwise an
% empty variable is returned). Additionally, coefficients of
% determination (R^2) are returned as R2TRAIN, R2TEST and R2VAL.
%
% Remarks:
%
% Each observation of the response variable y is assumed to be an unknown
% non-linear function of the corresponding observations of the predictor
% variables x1,..xn.
%
% Training data:
%
% The GPTIPS configuration file should populate the following required
% fields for the training data assuming 'Ntrain' observations on the
% input and output data. GP.USERDATA.XTRAIN should be a (Ntrain X n)
% matrix where the ith column contains the Ntrain observations of the ith
% input variable xi. GP.USERDATA.YTRAIN should be a (Ntrain x 1) vector
% containing the corresponding observations of the response variable y.
%
% Testing data:
%
% The following fields are optional and may be used, post-run, to see how
% well evolved models generalise to an unseen test data set with Ntest
% observations. They do not affect the model building process.
% GP.USERDATA.XTEST should be a (Ntest X n) matrix where the ith column
% contains the Ntest observations of the ith input variable xi.
% GP.USERDATA.YTEST should be a (Ntest x 1) vector containing the
% corresponding observations of the response variable y.
%
% How multigene symbolic regression works:
%
% In multigene symbolic regression, each prediction of y is formed by the
% weighted output of each of the trees/genes in the multigene individual
% plus a bias term. The number (M) and structure of the trees is evolved
% automatically during a GPTIPS run (subject to user defined
% constraints).
%
% i.e. ypredtrain = c0 + c1*tree1 + ... + cM*treeM
%
% where c0 = bias term
% c1,..,cM are the weights
% M is the number of genes/trees comprising the current individual
%
% The weights (i.e. regression coefficients) are automatically determined
% by a least squares procedure for each multigene individual and are
% stored in GP.FITNESS.RETURNVALUES for future use.
%
% Remarks:
%
% Because the GP structure is modified within this function (i.e. the
% field GP.FITNESS.RETURNVALUES is used to store the computed weighting
% coefficients for each gene) the GP structure must be returned as an
% output argument.
%
% This fitness function is used for multigene symbolic regression for
% GPDEMO2, GPDEMO3 and GPDEMO4 (the configuration files for these are
% GPDEMO2_CONFIG.M and GPDEMO3_CONFIG.M respectively) but it can and
% should be used for the user's own non-linear regression problems.
%
% Copyright (c) 2009-2015 Dominic Searson
%
% GPTIPS 2
%
% See also REGRESSMULTI_FITFUN_VALIDATE, GPDEMO2_CONFIG, GPDEMO3_CONFIG,
% GPDEMO4_CONFIG, GPDEMO2, GPDEMO3
%defaults in case of early exit
theta=[];ypredtrain=[];fitnessTest=[];ypredtest=[];pvals=[];
r2train=[];r2test=[];r2val=[];geneOutputs=[];geneOutputsTest=[];
geneOutputsVal=[];
% process evalstr with regex to allow direct access to data matrices
pat = 'x(\d+)';
evalstr = regexprep(evalstr,pat,'gp.userdata.xtrain(:,$1)');
y = gp.userdata.ytrain;
numData = gp.userdata.numytrain;
numGenes = numel(evalstr);
%set up a matrix to store the tree outputs plus a bias column of ones
geneOutputs = ones(numData,numGenes+1);
%eval each gene in the current individual
for i = 1:numGenes
ind = i + 1;
eval(['geneOutputs(:,ind)=' evalstr{i} ';']);
%check for nonsensical answers and break out early with an 'inf' if so
if any(~isfinite(geneOutputs(:,ind))) || any(~isreal(geneOutputs(:,ind)))
fitness = Inf;
gp.fitness.returnvalues{gp.state.current_individual} = [];
return
end
end
%only calc. weighting coeffs during an actual run or if forced
if ~gp.state.run_completed || gp.state.force_compute_theta
%set gp.userdata.bootSample to true to resample data for weights computation
%prepare LS matrix
if gp.userdata.bootSample
sampleInds = bootsample(geneOutputs,gp.userdata.bootSampleSize);
goptrans = geneOutputs(sampleInds,:)';
prj = goptrans * geneOutputs(sampleInds,:);
ysample = y(sampleInds);
else
goptrans = geneOutputs';
prj = goptrans * geneOutputs;
end
%calculate tree weight coeffs using SVD based least squares
%normal equation
try
if gp.userdata.bootSample
theta = pinv(prj) * goptrans * ysample;
else
theta = pinv(prj) * goptrans * y;
end
catch
theta = [];
fitness = Inf;
gp.fitness.returnvalues{gp.state.current_individual} = [];
return;
end
%assign bad fitness if any coeffs NaN or Inf
if any(isinf(theta)) || any(isnan(theta))
theta = [];
fitness = Inf;
gp.fitness.returnvalues{gp.state.current_individual} = [];
return;
end
%write coeffs to returnvalues field for storage
gp.fitness.returnvalues{gp.state.current_individual} = theta;
else %if post-run, get stored coeffs from return value field
theta = gp.fitness.returnvalues{gp.state.current_individual};
end
%calc. prediction of full training data set using the estimated weights
ypredtrain = geneOutputs * theta;
%calculate RMS prediction error (fitness)
err = gp.userdata.ytrain - ypredtrain;
fitness = sqrt(((err'*err)/numData));
%--below is for post-run evaluation of models, it is not used during a GPTIPS run--
if gp.state.run_completed
%compute r2 for training data
r2train = 1 - sum( (gp.userdata.ytrain-ypredtrain).^2 )/sum( (gp.userdata.ytrain-mean(gp.userdata.ytrain)).^2 );
plotValidation = 0;
%process validation data if present
if (isfield(gp.userdata,'xval')) && (isfield(gp.userdata,'yval')) && ...
~isempty(gp.userdata.xval) && ~isempty(gp.userdata.yval)
plotValidation = 1;
evalstr = strrep(evalstr,'.xtrain','.xval');
yval = gp.userdata.yval;
numData = length(yval);
%set up a matrix to store the tree outputs plus a bias column of ones
geneOutputsVal = zeros(numData,numGenes + 1);
geneOutputsVal(:,1) = ones;
%eval each tree
for i=1:numGenes
ind = i+1;
eval(['geneOutputsVal(:,ind)=' evalstr{i} ';']);
end
ypredval = geneOutputsVal*theta; %create the prediction on the validation data
fitness_val = sqrt(mean((gp.userdata.yval - ypredval).^2));
%compute r2 for validation data
r2val = 1 - sum( (gp.userdata.yval - ypredval).^2 )/sum( (gp.userdata.yval - mean(gp.userdata.yval)).^2 );
evalstr = strrep(evalstr,'.xval','.xtrain');
else
r2val = [];
end %end of validation data calcs
%process test data if present
plotTest = 0;
if (isfield(gp.userdata,'xtest')) && (isfield(gp.userdata,'ytest')) && ...
~isempty(gp.userdata.xtest) && ~isempty(gp.userdata.ytest)
plotTest = 1;
evalstr = strrep(evalstr,'.xtrain','.xtest');
ytest = gp.userdata.ytest;
numData = length(ytest);
%set up a matrix to store the tree outputs plus a bias column of ones
geneOutputsTest = zeros(numData,numGenes+1);
geneOutputsTest(:,1) = ones;
%eval each tree
for i=1:numGenes
ind = i + 1;
eval(['geneOutputsTest(:,ind)=' evalstr{i} ';']);
end
ypredtest = geneOutputsTest * theta; %create the prediction on the testing data
fitnessTest = sqrt(mean((gp.userdata.ytest - ypredtest).^2));
%compute r2 for test data
r2test = 1 - sum( (gp.userdata.ytest - ypredtest).^2 )/sum( (gp.userdata.ytest - mean(gp.userdata.ytest)).^2 );
end
%calc statistical analysis of gene significance on training data
%(if stats toolbox is present)
if gp.userdata.stats && gp.info.toolbox.stats
% Regress tree outputs (and bias) against y train data and get stats
wstate = warning;warning off;
stats = regstats(y,geneOutputs(:,2:end));
warning(wstate);
pvals = stats.tstat.pval;
else
pvals = [];
end
end
%if graphs required
if gp.state.run_completed && gp.userdata.showgraphs
if ~isempty(gp.userdata.name)
setname = ['Data: ' gp.userdata.name];
else
setname='';
end
%model predictions plots
figure('name','GPTIPS 2 Multigene regression. Model predictions.','numbertitle','off');
subplot(1+plotTest+plotValidation,1,1);
plot(ypredtrain,'Color',[0.85 0.33 0.1]);
hold on;
plot(gp.userdata.ytrain,'Color',[0 0.45 0.74]);
axis tight;
ylabel('y');
xlabel('Data point');
legend('Predicted','Actual');
title({setname,...
['RMS training set error: ' num2str(fitness) ' R^2: ' num2str(r2train)]},'interpreter','tex');
hold off;
if plotTest
subplot(2+plotValidation,1,2);
plot(ypredtest,'Color',[0.85 0.33 0.1]);
hold on;
plot(gp.userdata.ytest,'Color',[0 0.45 0.74]);
axis tight;
ylabel('y');
xlabel('Data point');
title(['RMS test set error: ' num2str(fitnessTest) ' R^2: ' num2str(r2test)],'interpreter','tex');
hold off
end
if plotValidation
subplot(2+plotValidation,1,3);
plot(ypredval,'Color',[0.85 0.33 0.1]);
hold on;
plot(gp.userdata.yval,'Color',[0 0.45 0.74]);
axis tight;
ylabel('y');
xlabel('Data point');
title(['RMS validation set error: ' num2str(fitness_val) ' R^2: ' num2str(r2val)],'interpreter','tex');
hold off
end
%scatterplots
scatterFig = figure('name','GPTIPS 2 Multigene regression. Model prediction scatterplot.','numbertitle','off');
subplot(1+plotTest+plotValidation,1,1);
minval = min([gp.userdata.ytrain;ypredtrain]);
maxval = max([gp.userdata.ytrain;ypredtrain]);
axis([minval maxval minval maxval]);
ilineTr = line([minval maxval], [minval maxval]);
set(ilineTr,'color','black','LineWidth',1);hold on;
scatter(gp.userdata.ytrain,ypredtrain,'o','MarkerFaceColor',[0 0.45 0.74],'MarkerEdgeColor','none');
box on;grid on;hold off;
ylabel('Predicted');
xlabel('Actual');
title({setname,['RMS training set error: ' num2str(fitness) ' R^2: ' num2str(r2train)]},'interpreter','tex');
%add scatter plot for test data, if present
if plotTest
subplot(2+plotValidation,1,2);
minval = min([gp.userdata.ytest;ypredtest]);
maxval = max([gp.userdata.ytest;ypredtest]);
axis([minval maxval minval maxval]);
ilineTest = line([minval maxval], [minval maxval]);
set(ilineTest,'color','black','LineWidth',1);hold on;
scatter(gp.userdata.ytest,ypredtest,'o','MarkerFaceColor',[0 0.45 0.74],'MarkerEdgeColor','none');
box on;grid on;hold off;
ylabel('Predicted');
xlabel('Actual');
title(['RMS test set error: ' num2str(fitnessTest) ' R^2: ' num2str(r2test)],'interpreter','tex');
end
%add scatter plot for validation data, if present
if plotValidation
figure(scatterFig);
subplot(2+plotTest,1,2+plotTest);
minval = min([gp.userdata.yval;ypredval]);
maxval = max([gp.userdata.yval;ypredval]);
axis([minval maxval minval maxval]);
ilineVal = line([minval maxval], [minval maxval]);
set(ilineVal,'color','black','LineWidth',1);hold on;
scatter(gp.userdata.yval,ypredval,'o','MarkerFaceColor',[0 0.45 0.74],'MarkerEdgeColor','none');
box on;grid on;hold off;
title(['RMS validation set error: ' num2str(fitness_val) ' R^2: ' num2str(r2val)],'interpreter','tex');
ylabel('Predicted');xlabel('Actual');
end
%gene weights & significance
if gp.info.toolbox.stats && gp.userdata.stats
%generate x labels for bar graphs
geneLabels = {'Bias'};
for i = 1:numGenes
geneLabels{i+1} = ['Gene ' int2str(i)];
end
%plot gene weights and offset
statFig = figure; coeffsAx = subplot(2,1,1);
set(statFig,'name','GPTIPS 2 P-values of model genes (on training data)','numbertitle','off');
geneBar = bar(coeffsAx,stats.beta);
set(coeffsAx,'xtick',1:(numGenes+1));
set(coeffsAx,'xticklabel',geneLabels);
title(coeffsAx,{setname,'Gene weights'});
%plot p-vals
pvalsAx = subplot(2,1,2);
pvalBar = bar(pvalsAx,stats.tstat.pval);
if ~verLessThan('matlab','8.4') %R2014b
pvalBar.FaceColor = [0 0.45 0.74];
pvalBar.BaseLine.Visible = 'off';
geneBar.FaceColor = [0 0.45 0.74];
else
pvalsBars = get(pvalsAx,'Children');
set(pvalsBars,'FaceColor',[0 0.45 0.74],'ShowBaseLine','off');
coeffsBars = get(coeffsAx,'Children');
set(coeffsBars,'FaceColor',[0 0.45 0.74]);
end
set(pvalsAx,'xtick',1:(numGenes+1));
set(pvalsAx,'xticklabel',geneLabels);
title(pvalsAx,'P value');xlabel(['R^2 = ' num2str(r2train)]);
end
end