Then, we decompose the weight vector u l for problem l into two parts: one part that models the distribution knowledge specific to each problem l and one part that models the common predictive structure, where w l and v l are weight vectors specific to each prediction problem l. Then, the parameters Θ, w l and v l can be learned by joint empirical risk minimization, i.e., by minimizing the joint empirical loss of the predictors for the K problems on the training instances as Eq.
5, It shows that w l and v l are estimated on n (l) training instances of problem l. Θ is estimated on all the training instances of the K problems.