A new algorithm for inference in HMM's with lower span complexity

The maximum likelihood problem for Hidden Markov Models is usually numerically solved by the Baum-Welch algorithm, which uses the Expectation-Maximization algorithm to find the estimates of the parameters. This algorithm has a recursion depth equal to the data sample size and cannot be computed in parallel, which limits the use of modern GPUs to speed up computation time. A new algorithm is proposed that provides the same estimates as the Baum-Welch algorithm, requiring about the same number of iterations, but is designed in such a way that it can be parallelized. As a consequence, it leads to a significant reduction in the computation time. This reduction is illustrated by means of numerical examples, where we consider simulated data as well as real datasets.