Multiclass Sparse Bayesian Regression for fMRI-Based Prediction

Algorithm 2

Gibbs-MCBR algorithm.

Initialize 𝛼₁, 𝛼₂, 𝜆₁, 𝜆₂ and 𝜂_𝑘

Randomly initialize 𝑧

Set a number of iterations burn number for burn-in

Set a number of iterations max steps

Repeat

 Compute Σ using (B.1) and 𝜇 using (B.2).

 Sample 𝐰 in 𝒩(𝐰∣𝜇,𝚺).

 Compute 𝑙₁ using (B.3) and 𝑙₂ using (B.4).

 Sample 𝜆 in ∏^{𝑘=𝐾𝑘=1}Γ(𝜆_𝑘∣𝑙_1,𝑘,𝑙_2,𝑘).

 Compute 𝑎₁ using (B.5) and 𝑎₂ using (B.6).

 Sample 𝛼 in Γ(𝑎₁,𝑎₂).

 Compute 𝜌_𝑗𝑘 using (B.7).

 Sample 𝐳 in mult(exp𝜌_𝑗,1,…,exp𝜌_𝑗,𝐾).

 Compute 𝑑_𝑘 using (B.8).

 Sample 𝜋_𝑘 in Dir(𝑑_𝑘).

until max steps;

return Average value of w after burn number iterations.