Contents

approx_expected_value.m

From A First Course in Machine Learning, Chapter 2. Simon Rogers, 31/10/11 [simon.rogers@glasgow.ac.uk] Approximating expected values via sampling

clear all;close all;

We are trying to compute the expected value of

$y^2$

Where $p(y)=U(0,1)$

Which is given by: $\int y^2 p(y) dy$

The analytic result is: $\frac{1}{3}$

Generate samples

ys = rand(10000,1);
% compute the expectation
ey2 = mean(ys.^2);
fprintf('\nSample-based approximation: %g',ey2);

Sample-based approximation: 0.333164

Look at the evolution of the approximation

posns = [1:10:length(ys)];
ey2_evol = zeros(size(posns));
for i = 1:length(posns)
    ey2_evol(i) = mean(ys(1:posns(i)).^2);
end
figure(1);hold off
plot(posns,ey2_evol);
hold on
plot([posns(1) posns(end)],[1/3 1/3],'r--');
xlabel('Samples');
ylabel('Approximation');


Published with MATLAB® 7.12