We propose to estimate the head-pose angles (pitch, yaw, and roll) by simultaneously predicting the pose parameters from observed high-dimensional feature vectors, and tracking these parameters over time. This is achieved by embedding a Gaussian mixture of linear inverse-regression model into a dynamic Bayesian model. The use of a switching Kalman filter (SKF) enables a principled way of carrying out this embedding. The SKF governs the temporal predic-tive distribution of the pose parameters (modeled as continuous latent variables) conditioned by the discrete variables associated with the mixture of linear inverse-regression formulation. We formally derive the equations of the proposed switching linear regression model, we propose an approximation that is both identifiable and computation-ally tractable, we design an EM procedure to estimate the SKF parameters in closed-form, and we carry out experiments and comparisons with other methods using recently released datasets.