d_{i=1}^{K} \text{MultiNormal}(y_i|0,w_i^{-1} LL^{\top}), \]</span>
where <span class="math inline">\(y_i\)</span> is the <span class="math inline">\(i\)</span>th row of <span class="math inline">\(y\)</span>. This is used to efficiently
handle Gaussian Processes with multi-variate outputs where only the
output dimensions share a kernel function but vary based on their
scale. If the model allows parameterization in terms of Cholesky
factor of the kernel matrix, this distribution is also more efficient
than 