Algorithm 1.

Bayesian Switching Factor Analysis

step 1: initialization

• set the number of states, K (the initial value of K is usually set to a large value, and during learning those states with small contributions will get weights close to zero);

• set the intrinsic dimensionality of the latent subspace, P, (in general P is set to be smaller than data dimension, P < D, however, in a fully noninformative initialization, one can simply set P = D − 1);,

• set the prior distribution parameters (Appendix A);

• initialize ${\langle {\mathit{z}}_t^s\rangle }_{q({\mathit{z}}_t^s)}$ (e.g., using K-means algorithm, with Euclidean distance as the similarity measure);

repeat

step 2: optimization of the model parameters (variational-maximization step)

• update q(ϕ) and $q({\mathit{x}}_{\mathit{\text{kt}}}^s)$ using update Equations (B.4), (B.5) and (B.11);

• update q(θ) using update Equations (B.2), (B.3);

step 3: optimization of the latent state variables (variational-expectation step)

• update ${\langle {\mathit{z}}_t^s\rangle }_{q({\mathit{z}}_t^s)}$ using update Equation (D.7);

• update ${\langle {\mathit{z}}_t^s{\mathit{z}}_{t-1}^s\rangle }_{q({\mathit{z}}_t^s)}$ using update Equation (D.8);

step 4: optimization of the posterior hyperparameters

• update posterior hyperparameters using Equations (E.2)–(E.6);

step 5: check for convergence

• evaluate lower bound, ℒ, from Equation (10) using Equation (F.1).

until convergence (ℒiter − ℒiter − 1 < thr)