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Copy pathgenerate_data_1D.m
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generate_data_1D.m
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function [x,z, xstar, fstar_true, z_type, range_star] = generate_data_1D(example, N, z_marginal, viz, zstar, rs, a)
if nargin < 6
rs = 5;
end
if nargin < 7
a = 0;
end
rng(rs)
z_type = 'c';
switch z_marginal % try different marginal distributions for z...
case 'uniform'
z = rand(1,N);
case 'normal'
z = randn(1,N);
case 'skewed'
z = rand(1,N).^3;
case 'bimodal'
z = [randn(1,round(N/3))+2, randn(1,round(N/3*2))-2];
case 'beta'
z = betarnd(2,3,1,N);
% z = betarnd(0.5,0.5,1,N);
% z = betarnd(0.5,1,1,N);
case 'categorical'
z = [zeros(1,round(N/20)), ones(1,round(N/10)), 2*ones(1,round(N/4)), 3*ones(1,round(N/5)), 4*ones(1,round(N/4) )];
z = [z, 5*ones(1, round(N/10) )];
z = [z, 6*ones(1, N-length(z)) ];
z = 1-z;
z_type = 'd';
z = z(randperm(N));
case 'categorical2'
z = [zeros(1,round(N/10)), ones(1,round(6*N/20)), 2*ones(1,round(N/5)), 3*ones(1,round(N/20*6) )];
z = [z, 4*ones(1, N-length(z)) ];
z = 1-z;
z_type = 'd';
z = z(randperm(N));
end
z = (z-min(z')')/(max(z')-min(z'))'; % normalize z to [0,1]
% zstar = quantile(z,0.2);
% zstar = 1.2%0.99%[0.1,0.4, 0.9];
% zstar = 0.9;
xstar = zeros(1,N);
switch example
case 0
f=@(z) 0*z;
g=@(z) 0.5*cos(4*pi*z + pi/4) + 0.55;
x= f(z) + randn(1,N).*g(z);
for l = 1:size(zstar,2)
xstar(l,:) = f(zstar(l)) + randn(1,N).*g(zstar(l));
end
fstar_true = @(x,zstar) normpdf(x,f(zstar),g(zstar));
range_star = @(zstar) [f(zstar) - 6*g(zstar), f(zstar) + 6*g(zstar)];
case 1
f=@(z) -sin(2*pi*z);
g=@(z) 0.5*z + 0.05;
x= f(z) + randn(1,N).*g(z);
for l = 1:size(zstar,2)
xstar(l,:) = f(zstar(l)) + randn(1,N).*g(zstar(l));
end
fstar_true = @(x,zstar) normpdf(x,f(zstar),g(zstar));
range_star = @(zstar) [f(zstar) - 6*g(zstar), f(zstar) + 6*g(zstar)];
case 2
f=@(z) -sin(2*pi*z);
g=@(z) 0.2 + 0*z;
x= f(z) + randn(1,N).*g(z);
x = x.^3;
for l = 1:size(zstar,2)
xstar(l,:) = f(zstar(l)) + randn(1,N).*g(zstar(l));
xstar(l,:) = xstar(l,:).^3;
end
fstar_true = @(x,zstar) normpdf( sign(x).*power(abs(x),1/3),f(zstar),g(zstar)).*(1/3.*power(abs(x) +1E-3,-2/3));
range_star = @(zstar) [f(zstar) - 6*g(zstar), f(zstar) + 6*g(zstar)].^3;
case 3
x = trnd( 3*z + 1.1, 1, N);
xstar = [];
fstar_true = @(x,zstar) tpdf( x, 3*zstar + 1.1);
range_star = @(zstar) [-6,6];
case 4
x = 5*(tanh( 2*( z-1/2) )).*randn(1,N);
for l = 1:size(zstar,2)
xstar(l,:) = 5*(tanh( 2*( zstar(l)-1/2) )).*randn(1,N);
end
fstar_true = @(x,zstar) normpdf(x,0, 5*abs((tanh( 2*( zstar-1/2) ))) );
case 5
a = rand(1,N);
w = randn(1,N);
x = (a<1/2).*(z<1/2).*(2+tanh(5*z-5/2)) + (a>1/2).*(-tanh(5*z-5/2)) +...
+ (a<1/2).*(z>1/2).*(tanh(5*z-5/2)-2);
x = x + w*0.15;
for l = 1:size(zstar,2)
xstar(l,:) = (a<1/2).*(zstar(l)<1/2).*(2+tanh(5*zstar(l)-5/2)) + (a>1/2).*(-tanh(5*zstar(l)-5/2)) +...
+ (a<1/2).*(zstar(l)>1/2).*(tanh(5*zstar(l)-5/2)-2);
xstar(l,:) = xstar(l,:)+w*0.15;
end
fstar_true = @(x,zstar) 1/2*normpdf(x,-tanh(5*zstar-5/2),0.15) + ...
+ 1/2*normpdf( x, (zstar<1/2).*(2+tanh(5*zstar-5/2)) + (zstar>1/2).*(tanh(5*zstar-5/2)-2),0.15);
case 6
a = rand(1,N);
w = .2*randn(1,N);
g = @(z) z+1/4;
x = (a < 0.3 ).*w + (a > 0.3 ).*(2 + w ) ;
x = x.*g(z);
xstar = [];
fstar_true = @(x,zstar) 0.3.*normpdf(x,0,.2*g(zstar))+...
+ 0.7.*normpdf(x,2*g(zstar),.2*g(zstar));
range_star = @(zstar) [ -6*.2*g(zstar), 2*g(zstar)+6*.2*g(zstar) ];
case 7
x = (0.5*abs(cos(2*pi*z))+0.05).*randn(1,N);
for l = 1:size(zstar,2)
xstar(l,:) = (0.5*abs(cos(2*pi*zstar(l))) + 0.05).*randn(1,N);
end
fstar_true = @(x,zstar) normpdf( x,0, abs(0.5*cos(2*pi*zstar))+0.05 );
case 8
x = randn(1,N);
ra = rand(1,N);
x = x + (-0.4*x + a*(1-z)).*(ra<1/8) + (-0.4*x -a*(1-z)).*(ra>7/8);
for l = 1:size(zstar,2)
xstar(l,:) = randn(1,N);
xstar(l,:) = xstar(l,:) + (-0.4*xstar(l,:) + a*(1-zstar(l))).*(ra<1/8) +(-0.4*xstar(l,:) -a*(1-zstar(l))).*(ra>7/8);
end
fstar_true = @(x,zstar) 1/8.*normpdf(x,-a*(1-zstar),0.6) + 1/8.*normpdf(x,a*(1-zstar),0.6) + 3/4*normpdf(x,0,1);
case 9
x = z + cos(pi*z) + 0.01*randn(1,N);
for l = 1:size(zstar,2)
xstar(l,:) = zstar(l) + cos(pi*zstar(l)) + 0.01*randn(1,N);
end
fstar_true = @(x,zstar) normpdf(x,zstar+cos(pi*zstar),0.01);
case 10
% designed for categorical, bimodal ver.
x = randn(1,N);
ra = rand(1,N);
x = x + (-0.4.*x + a*(1-z)).*(ra<1/8) + (-0.4.*x -a*(1-z)).*(ra>7/8);
g = @(z) ( z + 2)/3;
x = x.*g(z);
idx = randperm(N);
x(idx(1:round(N/2))) = x(idx(1:round(N/2))) + 5;
for l = 1:size(zstar,2)
xstar(l,:) = randn(1,N);
xstar(l,:) = xstar(l,:) + (-0.4*xstar(l,:) + a*(1-zstar(l))).*(ra<1/8) +(-0.4*xstar(l,:) -a*(1-zstar(l))).*(ra>7/8);
end
fstar_true_first = @(x,zstar) 1/8.*normpdf(x,-a*(1-zstar).*g(zstar),0.6*g(zstar) ) + 1/8.*normpdf(x,a*(1-zstar).*g(zstar),0.6.*g(zstar)) +...
+ 3/4*normpdf(x,0,1.*g(zstar));
fstar_true = @(x,zstar) 1/2*fstar_true_first(x,zstar) + 1/2*fstar_true_first(x-5,zstar);
range_star = @(zstar) g(zstar).*[-a*(1-zstar)-1.8, a*(1-zstar) + 1.8];
range_star = @(zstar) [-5,10];
case 11
% designed for categorical
x = randn(1,N);
ra = rand(1,N);
x = x + (-0.4.*x + a*(1-z)).*(ra<1/8) + (-0.4.*x -a*(1-z)).*(ra>7/8);
g = @(z) ( z + 2)/3;
x = x.*g(z);
for l = 1:size(zstar,2)
xstar(l,:) = randn(1,N);
xstar(l,:) = xstar(l,:) + (-0.4*xstar(l,:) + a*(1-zstar(l))).*(ra<1/8) +(-0.4*xstar(l,:) -a*(1-zstar(l))).*(ra>7/8);
end
fstar_true = @(x,zstar) 1/8.*normpdf(x,-a*(1-zstar).*g(zstar),0.6*g(zstar) ) + 1/8.*normpdf(x,a*(1-zstar).*g(zstar),0.6.*g(zstar)) +...
+ 3/4*normpdf(x,0,1.*g(zstar));
range_star = @(zstar) g(zstar).*[-a*(1-zstar)-1.8, a*(1-zstar) + 1.8];
range_star = @(zstar) [-3.5,3.5];
case 12
% smoothness 1
g=@(z) tanh(10*(z-0.5))+1.5;
x = randn(1,N).*g(z) + 10*tanh(10*(z-0.5));
fstar_true = @(x,zstar) normpdf( x, 10*tanh(10*(zstar-0.5)), g(zstar)) ;
range_star = @(zstar) [-22,22];
range_star = @(zstar) 10*tanh(10*(zstar-0.5)) + 6*[-g(zstar), g(zstar)];
case 13
% smoothness 2
g = @(z) tanh(10*(z-0.5))+1.5;
x = g(z).*randn(1,N) + 20*(heaviside(z-0.5)-0.5);
fstar_true = @(x,zstar) normpdf( x, 20*(heaviside(zstar-0.5)-0.5), g(zstar) );
range_star = @(zstar) 20*(heaviside(zstar-0.5)-0.5) + 6*[-g(zstar), g(zstar)];
case 14
g = @(z) 3*tanh(10*(z-0.5));%+1.5;
%xs = rand(1,N);
%x = sqrt(xs)-1 ; idxx = randperm(N); x(idxx(1:round(N/2))) = -x(idxx(1:round(N/2)));
%x = x + g(z);g = @(z) tanh(10*(z-0.5))+1.5;
g_var = @(z) z + 1/4;
xs = rand(1,N);
x = sqrt(xs)-1 ; idxx = randperm(N); x(idxx(1:round(N/2))) = -x(idxx(1:round(N/2)));
x = g_var(z).*x + g(z);
f = @(x) (1-abs(x)).*( abs(x)<1);
fstar_true = @(x,zstar) f( (x - g(zstar))./g_var(zstar) )./g_var(zstar);
range_star = @(zstar) [g(zstar) - 2 - g_var(zstar), g(zstar)+2+g_var(zstar)];
%f = @(x) (1-abs(x)).*( abs(x)<1);
%fstar_true = @(x,zstar) f( x - g(zstar) );
%range_star = @(zstar) [g(zstar) - 2, g(zstar)+2];
end
if viz
figure;
scatter(z,x)
xlabel('$z$','interpreter','latex')
ylabel('$x$','interpreter','latex')
title('$x$ vs $z$','interpreter','latex')
set(gca,'fontsize',24)
yl = ylim;
hold on,
for l = 1:size(zstar,2)
plot(zstar(l)*ones(1,N),linspace(yl(1),yl(2),N),'k-.','linewidth',2)
end
leg=legend('data','$z^*$');
set(leg,'interpreter','latex')
ylim(yl);
set(gcf,'position',[-33 1160 560 420]);
end