A new constant memory recursion for hidden Markov models.

Area of Science:

• Statistics
• Machine Learning
• Time Series Analysis

Background:

• Hidden Markov (HM) models are widely used for analyzing sequential data.
• Traditional estimation algorithms like Baum-Welch have memory limitations that scale with data length.
• Existing methods may require numerical adjustments (renormalizations) and complex decoding procedures (e.g., Viterbi).

Purpose of the Study:

• To develop a novel recursion for hidden Markov models (HM) based on Bartolucci and Besag (2002).
• To implement an estimation algorithm with memory requirements independent of the observed data series length.
• To enable direct global decoding of latent states without Viterbi, reducing computational complexity.

Main Methods:

• Developed a new recursion to compute the conditional distribution of latent states.
• Implemented an estimation algorithm leveraging this recursion, achieving constant memory usage.
• Compared the proposed algorithm with Baum-Welch and the Churbanov-Winters-Hilt linear memory algorithm via simulations.

Main Results:

• The proposed algorithm requires memory independent of the time-series length.
• It avoids numerical renormalization issues common in other methods.
• Direct global decoding is achieved, outperforming Viterbi in memory efficiency.

Conclusions:

• The novel recursion provides a memory-efficient approach for HM model estimation and decoding.
• This method offers advantages over Baum-Welch and Viterbi, particularly for large datasets.
• Simulations confirm the computational and memory benefits for continuous time-series data.