Inferences on HMM
Maurice Charbit · 2016
Hidden Markov models (HMM) have a fundamental property that results in the existence of recursive algorithms, meaning that the number of operations and the size of the memory needed to calculate the required values do not increase with the number of samples. The best-known example of this is the Kalman filter. In cases where the states real random vector of finite dimension (Xn) of an HMM take their value in a finite set of values, the inference on Xn has a closed-form expression. This expression is based on two smoothing algorithms known as the Baum-Welch or forward-backward algorithms. The prediction and update expressions are intractable; however, there are two important cases in which closed-form expressions may be obtained. First, the linear Gaussian case leads to the Kalman filter. The second case arises when real random vector of finite dimension (Xn) takes its values in a finite state set.