. Author manuscript; available in PMC: 2017 Nov 30.

Published in final edited form as: IEEE Trans Pattern Anal Mach Intell. 2015 Dec 23;38(11):2269–2283. doi: 10.1109/TPAMI.2015.2511754

Algorithm 2.

MM-SGBN: Discriminative Learning

Input: data X₁,X₂ ∈ ℝⁿ^×^m, label y ∈ ℝⁿ^×1

Denote Θ = [Θ₁,Θ₂]

Initialize Θ⁽⁰⁾, o⁽⁰⁾,ϒ⁽⁰⁾ by Algorithm 3 for each class.

Fix Θ = Θ⁽⁰⁾ and estimate r⁽⁰⁾ and

ξ_{i}^{(0)}

only with the two constraints (3.11a) and (3.11b).

Initialize t = 1.

repeat

Step 1: Fixing o = o⁽^t⁻¹⁾ and ϒ = ϒ⁽^t⁻¹⁾, optimize Eqn. (3.11) with the constraints (3.11a ~ 3.11c) to update Θ⁽^t⁾, r⁽^t⁾ and $ε_{i}^{(t)}$ ;
Step 2: Fixing Θ⁽^t⁾, optimize Eqn. (4.2) to update o⁽^t⁾ and ϒ⁽^t⁾ to enforce DAG.

Let t = t + 1

until convergence/max number of iterations

Output: Θ^★ = Θ⁽^t⁾