title: Scikit-learn: How to specify multiple input kernels in gaussian process regression?
body: <p>This is what I am trying:</p>
  <pre><code>kernel = C(np.ones(11), (1e-3, 1e3)) * RBF(length_scale=np.ones(11), length_scale_bounds=(1e-5, 1e3)) + WhiteKernel(
      noise_level=np.array(11*[1e-4]), noise_level_bounds=(1e-5, 1)) 
  gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=9, normalize_y=True )
  </code></pre>
  <p>and this is the error I am getting:</p>
  <pre><code>    286     # unbounded variables must use None, not +-inf, for the optimizer to work properly
  ValueError: length of x0 != length of bounds
  </code></pre>
  <p>But when I try the following, it works:</p>
  <pre><code>kernel = C(1.0, (1e-3, 1e3)) * RBF(length_scale=np.ones(11), length_scale_bounds=(1e-5, 1e3)) + WhiteKernel(
  noise_level=1, noise_level_bounds=(1e-5, 1)) 
  </code></pre>
  <p>However, I would like to try the first kernel as I have 11 inputs and 8 outputs and I want better predictions from my gp.</p>