Gaussian Process, negative hyper-parameters? <p>I'm doing Gaussian Processes for Regression using GPML toolbox. However, after optimization using 'minimize.m' (without mean functions), I get some negative hyper-parameters! </p> <p>The initial hyper-parameters are: </p> <p><code>hyp.cov = [0; 0]; % two hyper-parameters in covariance kernel (length-scale &amp; amplitute) hyp.lik = log(0.1); %hyper-parameters of noise</code></p> <p>The original training data:</p> <pre><code>x=[819 1119 1419 1599 1719 1839 1899 2019 2079 2139]; %coordinates y=[105.00 114.33 126.33 130.33 116.33 103.00 103.00 124.67 122.67 109.00]; %training data </code></pre> <p>In my codes, y are <strong>NORMALIZED</strong> to have zero mean and unit variance. Then optimize:</p> <pre><code>hyp = minimize(hyp, @gp, -100, @infExact, [], {@covSEiso}, likfunc, x,y); </code></pre> <p>After about 100 iterations, I get some negative hyper-parameters!!! It is quite confusing....</p> <p>However, if I don't normalize y, all hyper-parameters will be positive after optimization.</p> <p>Could anyone tell me what does Negative Hyper-parameters mean? Should I normalize the data?</p>