Figure 2
The diagram illustrates a second-order hidden Markov model (HMM) dependency graph. It consists of three main circles labeled z subscript t-2, z subscript t-1, and z subscript t, representing hidden states at different time steps. Below each circle, there are rectangles labeled x subscript t-2, x subscript t-1, and x subscript t, representing the obesrvation emitted at thattime step. Blue solid arrows connect z subscript t-2 to z subscript t-1, and z subscript t-1 to z subscript t, indicating standard Markovian transitions from t-1 to t. Curved red dashed arrows skip one time step: one runs from z subscript t-2 directly to z subscript t, and a second continues from z subscript t-1 to the next state beyond t, indicated by the ellipsis at the right. These arrows are labeled Order 2, Momentum and represent the second order memory transitions from t-2 to t. The diagram also includes a legend explaining the blue solid arrows as standard Markov transitions and the red dashed arrows as second-order memory transitions.Dependency graph of the second-order HMM (Mari et al., 1997)