Algorithm 1.

Learn the LDS model in gLDS.

INPUT:
• Initialization A(0), C(0), Z(0).
• Hyper-parameters, γ, λ, β and α.
• A collection of MTS sequences Y1, ⋯, YN.
PROCEDURE:
1:	// Optimize A, C and Z
2:	repeat
3:	Update A by solving eq.(3.7).
4:	Update C by solving eq.(3.8).
5:	for m: 1 → N do
6:	Update ${\mathbf{z}}_1^m$ by solving eq.(3.10).
7:	for t: 2 → Tm − 1 do
8:	Update ${\mathbf{z}}_t^m$ by solving eq.(3.11).
9:	end for
10:	Update ${\mathbf{z}}_{T_m}^m$ by solving eq.(3.12).
11:	end for
12:	until Convergence
13:	// Optimize Q̂, R̂, ξ̂, Ψ̂
14:	Compute Q̂, R̂, ξ̂, Ψ̂ using eqs.(3.13 – 3.16).
OUTPUT:
• Learned LDS parameters: Ω̂ = {Â, Ĉ, Q̂, R̂, ξ̂, Ψ̂}.