Algorithm 1: MT-CoReg Algorithm: alternate minimization are performed, which consist of successive multi-task regression problems.

$$\begin{array}{cc}\hfill & 1:\mathbf{Input}:\text{Standardized data matrices}{\mathbf{X}}_1,{\mathbf{X}}_2,\text{phenotype}\hfill \\ \hfill & \text{vector y},\text{and}\text{parameters}\lambda ,\gamma .\hfill \\ \hfill & 2:\mathbf{Initialize}:{\alpha }_1,..,{\alpha }_M\text{using ridge regression and}{\beta }_1,..,{\beta }_M\hfill \\ \hfill & \text{using ridge CCA}.\hfill \\ \hfill & 3:\mathbf{for}k=0\text{to Convergence}\mathbf{do}\hfill \\ \hfill & 4:\mathbf{for}m=1:1:M\mathbf{do}\hfill \\ \hfill & 5:\text{Solve for}{\beta }_m=[{\alpha }_m,{\theta }_m]\hfill \\ \hfill & \underset{{\beta }_m}{\text{min}}J({\beta }_m\mid {\beta }_{[1:M]\setminus m]}^{\ast })=\Vert {\tilde{\mathbf{y}}}_m-{\tilde{\mathbf{X}}}_m{\alpha }_m{\Vert }_2^2\hfill \\ \hfill & +\sum _{\begin{array}{c}\hfill q=1\hfill \\ \hfill q\ne m\hfill \end{array}}^M\Vert {\widehat{\mathbf{y}}}_q-{\widehat{\mathbf{X}}}_m{\theta }_m{\Vert }_2^2+\lambda \sum _{i=1}^{p_m}\Vert {\beta }_m^i{\Vert }_2(10)\hfill \\ \hfill & \text{where}\hfill \\ \hfill & \left\{\begin{array}{cc}{\tilde{\mathbf{y}}}_m=\hfill & \sqrt{(1-\gamma )}\mathbf{y}\hfill \\ {\widehat{\mathbf{y}}}_q=\hfill & \sqrt{\gamma }{\mathbf{X}}_q{\theta }_q^{\ast }\hfill \end{array}\phantom{\}}\text{and}\right\{\begin{array}{cc}{\tilde{\mathbf{X}}}_m=\hfill & \sqrt{(1-\gamma )}{\mathbf{X}}_m\hfill \\ {\widehat{\mathbf{X}}}_m=\hfill & \sqrt{\gamma }{\mathbf{X}}_m\hfill \end{array}\phantom{\}}(11)\hfill \\ \hfill & 6:\mathrm{end}\mathrm{for}\hfill \\ \hfill & 7:\mathrm{end}\mathrm{for}\hfill \end{array}$$